메뉴 건너뛰기




Volumn 43, Issue 1-3, 2007, Pages 1-41

High-order methods for the Euler and Navier-Stokes equations on unstructured grids

Author keywords

CFD; Euler equations; High order; Navier Stokes; Unstructured grids

Indexed keywords

AEROSPACE ENGINEERING; COMPUTATIONAL FLUID DYNAMICS; COMPUTATIONAL METHODS; COMPUTER SIMULATION; LARGE EDDY SIMULATION; NAVIER STOKES EQUATIONS; PROBLEM SOLVING; WAVE PROPAGATION;

EID: 34547093896     PISSN: 03760421     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.paerosci.2007.05.001     Document Type: Review
Times cited : (291)

References (166)
  • 2
    • 33745005954 scopus 로고    scopus 로고
    • Expectations for computational fluid dynamics
    • Vassberg J.C. Expectations for computational fluid dynamics. Int J Comput Fluid Dyn 19 8 (2005) 549-558
    • (2005) Int J Comput Fluid Dyn , vol.19 , Issue.8 , pp. 549-558
    • Vassberg, J.C.1
  • 3
    • 0029482553 scopus 로고
    • Behavior of linear reconstruction techniques on unstructured meshes
    • Aftosmis M., Gaitonde D., and Tavares T.S. Behavior of linear reconstruction techniques on unstructured meshes. AIAA J 33 11 (1995) 2038-2049
    • (1995) AIAA J , vol.33 , Issue.11 , pp. 2038-2049
    • Aftosmis, M.1    Gaitonde, D.2    Tavares, T.S.3
  • 4
    • 0001875110 scopus 로고
    • A grid generation and flow solution method for the Euler equations on unstructured grids
    • Anderson W.K. A grid generation and flow solution method for the Euler equations on unstructured grids. J Comput Phys 110 (1994) 23-38
    • (1994) J Comput Phys , vol.110 , pp. 23-38
    • Anderson, W.K.1
  • 5
    • 34547097209 scopus 로고    scopus 로고
    • Barth TJ, Jespersen DC. The design and application of upwind schemes on unstructured meshes. AIAA Paper No. 89-0366, 1989.
  • 6
    • 34547096701 scopus 로고    scopus 로고
    • Frink NT. Recent progress toward a three dimensional unstructured Navier-Stokes flow solver. AIAA Paper No. 94-0061, 1994.
  • 9
    • 33749583060 scopus 로고
    • Flux corrected transport,1 SHASTA, a fluid transport algorithm that works
    • Boris J.P., and Book D.L. Flux corrected transport,1 SHASTA, a fluid transport algorithm that works. J Comput Phys A 11 (1973) 38-69
    • (1973) J Comput Phys A , vol.11 , pp. 38-69
    • Boris, J.P.1    Book, D.L.2
  • 10
    • 40749159424 scopus 로고
    • High resolution schemes for hyperbolic conservation laws
    • Harten A. High resolution schemes for hyperbolic conservation laws. J Comput Phys 49 (1983) 357-393
    • (1983) J Comput Phys , vol.49 , pp. 357-393
    • Harten, A.1
  • 11
    • 49049151571 scopus 로고
    • Flux vector splitting of the inviscid gas dynamics equations with application to finite difference methods
    • Steger J.L., and Warming R.F. Flux vector splitting of the inviscid gas dynamics equations with application to finite difference methods. J Comput Phys 40 (1981) 263
    • (1981) J Comput Phys , vol.40 , pp. 263
    • Steger, J.L.1    Warming, R.F.2
  • 12
    • 0028407037 scopus 로고
    • Parallel, adaptive finite element methods for conservation laws
    • Biswas R., Devine K.D., and Flaherty J.E. Parallel, adaptive finite element methods for conservation laws. Appl Numer Math 14 (1994) 255-283
    • (1994) Appl Numer Math , vol.14 , pp. 255-283
    • Biswas, R.1    Devine, K.D.2    Flaherty, J.E.3
  • 13
    • 34547130772 scopus 로고    scopus 로고
    • Hassan O, Morgan K, Peraire J. An implicit finite element method for high speed flows. AIAA Paper No. 90-0402, January 1990.
  • 14
    • 0023525478 scopus 로고
    • Recent progress in the development and understanding of SUPG methods with special reference to the compressible Euler and Navier-Stokes equations
    • Hughes T.J.R. Recent progress in the development and understanding of SUPG methods with special reference to the compressible Euler and Navier-Stokes equations. Int J Numer Methods Fluids 7 (1987) 1261-1275
    • (1987) Int J Numer Methods Fluids , vol.7 , pp. 1261-1275
    • Hughes, T.J.R.1
  • 15
    • 45149144830 scopus 로고
    • A new finite element formulation for computational fluid dynamics: VIII. The Galerkin least squares method for advective-diffusive equations
    • Hughes T.J.R., Franca L.P., and Hulbert G.M. A new finite element formulation for computational fluid dynamics: VIII. The Galerkin least squares method for advective-diffusive equations. Comput Methods Appl Mech Eng 73 (1989) 173-189
    • (1989) Comput Methods Appl Mech Eng , vol.73 , pp. 173-189
    • Hughes, T.J.R.1    Franca, L.P.2    Hulbert, G.M.3
  • 16
    • 0022811673 scopus 로고
    • A new finite element formulation for CFD: IV. A discontinuity-capturing operator for multidimensional advective-diffusive systems
    • Hughes T.J.R., and Mallet M. A new finite element formulation for CFD: IV. A discontinuity-capturing operator for multidimensional advective-diffusive systems. Comput Methods Appl Mech Eng 58 3 (1986) 329-356
    • (1986) Comput Methods Appl Mech Eng , vol.58 , Issue.3 , pp. 329-356
    • Hughes, T.J.R.1    Mallet, M.2
  • 17
    • 0001042498 scopus 로고
    • An adaptive finite element procedure for compressible high speed flows
    • Lohner R., Morgan K., and Zienkiewicz O.C. An adaptive finite element procedure for compressible high speed flows. Comput Methods Appl Mech Eng 51 (1985) 441-465
    • (1985) Comput Methods Appl Mech Eng , vol.51 , pp. 441-465
    • Lohner, R.1    Morgan, K.2    Zienkiewicz, O.C.3
  • 18
    • 0036743716 scopus 로고    scopus 로고
    • On the use of higher-order finite-difference schemes on curvilinear and deforming meshes
    • Visbal M.R., and Gaitonde D.V. On the use of higher-order finite-difference schemes on curvilinear and deforming meshes. J Comput Phys 181 1 (2002) 155-185
    • (2002) J Comput Phys , vol.181 , Issue.1 , pp. 155-185
    • Visbal, M.R.1    Gaitonde, D.V.2
  • 19
    • 27644472417 scopus 로고    scopus 로고
    • Progress and future prospects of CFD in aerospace-wind tunnel and beyond
    • Fujii K. Progress and future prospects of CFD in aerospace-wind tunnel and beyond. Prog Aerospace Sci 41 (2005) 455-470
    • (2005) Prog Aerospace Sci , vol.41 , pp. 455-470
    • Fujii, K.1
  • 20
    • 22844446543 scopus 로고    scopus 로고
    • High-order accurate, lownumerical diffusion methods for aerodynamics
    • Ekaterinaris J.A. High-order accurate, lownumerical diffusion methods for aerodynamics. Prog in Aerospace Sci 41 (2005) 192-300
    • (2005) Prog in Aerospace Sci , vol.41 , pp. 192-300
    • Ekaterinaris, J.A.1
  • 21
    • 84966246413 scopus 로고
    • TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework
    • Cockburn B., and Shu C.-W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework. Math Comput 52 (1989) 411-435
    • (1989) Math Comput , vol.52 , pp. 411-435
    • Cockburn, B.1    Shu, C.-W.2
  • 22
    • 0036570604 scopus 로고    scopus 로고
    • Spectral (finite) volume method for conservation laws on unstructured grids: basic formulation
    • Wang Z.J. Spectral (finite) volume method for conservation laws on unstructured grids: basic formulation. J Comput Phys 178 (2002) 210-251
    • (2002) J Comput Phys , vol.178 , pp. 210-251
    • Wang, Z.J.1
  • 23
    • 0036647456 scopus 로고    scopus 로고
    • Spectral (finite) volume method for conservation laws on unstructured grids II: extension to two-dimensional scalar equation
    • Wang Z.J., and Liu Y. Spectral (finite) volume method for conservation laws on unstructured grids II: extension to two-dimensional scalar equation. J Comput Phys 179 2 (2002) 665-697
    • (2002) J Comput Phys , vol.179 , Issue.2 , pp. 665-697
    • Wang, Z.J.1    Liu, Y.2
  • 26
    • 48549109395 scopus 로고
    • A spectral element method for fluid dynamics: laminar flow in a channel expansion
    • Patera A.T. A spectral element method for fluid dynamics: laminar flow in a channel expansion. J Comput Phys 54 (1984) 468-488
    • (1984) J Comput Phys , vol.54 , pp. 468-488
    • Patera, A.T.1
  • 27
    • 0000141828 scopus 로고    scopus 로고
    • A staggered-grid multidomain spectral method for the compressible Navier-Stokes equations
    • Kopriva D.A. A staggered-grid multidomain spectral method for the compressible Navier-Stokes equations. J Comput Phys 143 (1998) 125-148
    • (1998) J Comput Phys , vol.143 , pp. 125-148
    • Kopriva, D.A.1
  • 29
    • 0030295512 scopus 로고    scopus 로고
    • Spectral methods on arbitrary grids
    • Carpenter M.H., and Gottlieb D. Spectral methods on arbitrary grids. J Comput Phys 129 1 (1996) 74-86
    • (1996) J Comput Phys , vol.129 , Issue.1 , pp. 74-86
    • Carpenter, M.H.1    Gottlieb, D.2
  • 30
    • 0034503732 scopus 로고    scopus 로고
    • Stable spectral methods on tetrahedral elements
    • Hesthaven J.S., and Teng C.H. Stable spectral methods on tetrahedral elements. SIAM J Sci Comput 21 (2000) 2352-2380
    • (2000) SIAM J Sci Comput , vol.21 , pp. 2352-2380
    • Hesthaven, J.S.1    Teng, C.H.2
  • 31
    • 34547138856 scopus 로고    scopus 로고
    • Van Leer B, Nomura S. Discontinuous Galerkin for diffusion. AIAA Paper No. 2005-5108, 2005.
  • 32
    • 34547135891 scopus 로고    scopus 로고
    • Barth TJ, Frederickson PO. High-order solution of the Euler equations on unstructured grids using quadratic reconstruction. AIAA Paper No. 90-0013, 1990.
  • 33
    • 0000935266 scopus 로고
    • A finite-difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics
    • Godunov S.K. A finite-difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics. Mat Sb 47 (1959) 271
    • (1959) Mat Sb , vol.47 , pp. 271
    • Godunov, S.K.1
  • 34
    • 34249988639 scopus 로고
    • Towards the ultimate conservative difference scheme II. Monotonicity and conservation combined in a second-order scheme
    • Van Leer B. Towards the ultimate conservative difference scheme II. Monotonicity and conservation combined in a second-order scheme. J Comput Phys 14 (1974) 361
    • (1974) J Comput Phys , vol.14 , pp. 361
    • Van Leer, B.1
  • 35
    • 2442433925 scopus 로고
    • Towards the ultimate conservative difference scheme V. A second order sequel to Godunov's method
    • Van Leer B. Towards the ultimate conservative difference scheme V. A second order sequel to Godunov's method. J Comput Phys 32 (1979) 101-136
    • (1979) J Comput Phys , vol.32 , pp. 101-136
    • Van Leer, B.1
  • 36
    • 34547419627 scopus 로고
    • The piecewise parabolic method for gas-dynamical simulations
    • Colella P., and Woodward P. The piecewise parabolic method for gas-dynamical simulations. J Comput Phys 54 (1984)
    • (1984) J Comput Phys , vol.54
    • Colella, P.1    Woodward, P.2
  • 37
    • 33749725182 scopus 로고
    • Uniformly high-order essentially non-oscillatory schemes III
    • Harten A., Engquist B., Osher S., and Chakravarthy S. Uniformly high-order essentially non-oscillatory schemes III. J Comput Phys 71 (1987) 231
    • (1987) J Comput Phys , vol.71 , pp. 231
    • Harten, A.1    Engquist, B.2    Osher, S.3    Chakravarthy, S.4
  • 38
    • 0029656361 scopus 로고    scopus 로고
    • Three dimensional unstructured adaptive multigrid scheme for the Navier-Stokes equations
    • Braaten M.E., and Connell S.D. Three dimensional unstructured adaptive multigrid scheme for the Navier-Stokes equations. AIAA J 34 2 (1996) 281-290
    • (1996) AIAA J , vol.34 , Issue.2 , pp. 281-290
    • Braaten, M.E.1    Connell, S.D.2
  • 39
    • 34547118525 scopus 로고    scopus 로고
    • Jameson A, Baker TJ, Weatherill NP. Calculation of inviscid transonic flow over a complete aircraft. AIAA Paper 86-0103, 1986.
  • 40
    • 0030072004 scopus 로고    scopus 로고
    • Hybrid prismatic/tetrahedral grid generation for complex geometries
    • Kallinderis Y., Khawaja A., and McMorris H. Hybrid prismatic/tetrahedral grid generation for complex geometries. AIAA J 34 (1996) 291-298
    • (1996) AIAA J , vol.34 , pp. 291-298
    • Kallinderis, Y.1    Khawaja, A.2    McMorris, H.3
  • 41
    • 0024103736 scopus 로고
    • Generation of three-dimensional unstructured grids by the advancing front method
    • Lohner R., and Parikh P. Generation of three-dimensional unstructured grids by the advancing front method. Int J Numer Methods Fluids 8 (1988) 1135-1149
    • (1988) Int J Numer Methods Fluids , vol.8 , pp. 1135-1149
    • Lohner, R.1    Parikh, P.2
  • 42
    • 0001742674 scopus 로고    scopus 로고
    • Unstructured grid techniques
    • Mavriplis D.J. Unstructured grid techniques. Annu Rev Fluid Mech 29 (1997) 473-514
    • (1997) Annu Rev Fluid Mech , vol.29 , pp. 473-514
    • Mavriplis, D.J.1
  • 43
    • 0029707892 scopus 로고    scopus 로고
    • Three-dimensional unstructured viscous grids by the advancing-layers method
    • Pirzadeh S. Three-dimensional unstructured viscous grids by the advancing-layers method. AIAA J 34 1 (1996) 43-49
    • (1996) AIAA J , vol.34 , Issue.1 , pp. 43-49
    • Pirzadeh, S.1
  • 44
    • 0029656535 scopus 로고    scopus 로고
    • A perspective on unstructured grid flow solvers
    • Venkatakrishnan V. A perspective on unstructured grid flow solvers. AIAA J 34 3 (1996) 533-547
    • (1996) AIAA J , vol.34 , Issue.3 , pp. 533-547
    • Venkatakrishnan, V.1
  • 45
    • 34547103479 scopus 로고    scopus 로고
    • Wang ZJ, Chen RF. Anisotropic cartesian grid method for viscous turbulent flow. AIAA Paper No. 2000-0395, 2000.
  • 46
    • 0002677386 scopus 로고
    • On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation
    • Abgrall R. On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation. J Comput Phys 114 (1994) 45-58
    • (1994) J Comput Phys , vol.114 , pp. 45-58
    • Abgrall, R.1
  • 47
    • 0003018067 scopus 로고
    • Triangle based adaptive stencils for the solution of hyperbolic conservation laws
    • Durlofsky L.J., Enquist B., and Osher S. Triangle based adaptive stencils for the solution of hyperbolic conservation laws. J Comput Phys 98 (1992) 64
    • (1992) J Comput Phys , vol.98 , pp. 64
    • Durlofsky, L.J.1    Enquist, B.2    Osher, S.3
  • 48
    • 0031146386 scopus 로고    scopus 로고
    • Quasi-ENO schemes for unstructured meshes based on unlimited data-dependent least-squares reconstruction
    • Ollivier-Gooch C.F. Quasi-ENO schemes for unstructured meshes based on unlimited data-dependent least-squares reconstruction. J Comput Phys 133 (1997) 6-17
    • (1997) J Comput Phys , vol.133 , pp. 6-17
    • Ollivier-Gooch, C.F.1
  • 49
    • 0030738142 scopus 로고    scopus 로고
    • On the construction of essentially non-oscillatory finite volume approximations to hyperbolic conservation laws on general triangulations: polynomial recovery accuracy and stencil selection
    • Sonar T. On the construction of essentially non-oscillatory finite volume approximations to hyperbolic conservation laws on general triangulations: polynomial recovery accuracy and stencil selection. Comput Methods Appl Mech Eng 140 (1997) 157
    • (1997) Comput Methods Appl Mech Eng , vol.140 , pp. 157
    • Sonar, T.1
  • 50
    • 0000592595 scopus 로고
    • Weighted essentially non-oscillatory schemes
    • Liu X.D., Osher S., and Chan T. Weighted essentially non-oscillatory schemes. J Comput Phys 115 (1994) 200-212
    • (1994) J Comput Phys , vol.115 , pp. 200-212
    • Liu, X.D.1    Osher, S.2    Chan, T.3
  • 51
    • 0030161771 scopus 로고    scopus 로고
    • Efficient implementation of weighted ENO schemes
    • Jiang G., and Shu C.-W. Efficient implementation of weighted ENO schemes. J Comput Phys 126 (1996) 202
    • (1996) J Comput Phys , vol.126 , pp. 202
    • Jiang, G.1    Shu, C.-W.2
  • 52
    • 0001484343 scopus 로고    scopus 로고
    • Weighted essentially non-oscillatory schemes for the interpolation of mean values on unstructured grids
    • Friedrich O. Weighted essentially non-oscillatory schemes for the interpolation of mean values on unstructured grids. J Comput Phys 144 (1998) 194-212
    • (1998) J Comput Phys , vol.144 , pp. 194-212
    • Friedrich, O.1
  • 53
    • 0003140474 scopus 로고    scopus 로고
    • Weighted essentially non-oscillatory schemes on triangular meshes
    • Hu C., and Shu C.-W. Weighted essentially non-oscillatory schemes on triangular meshes. J Comput Phys 150 (1999) 97-127
    • (1999) J Comput Phys , vol.150 , pp. 97-127
    • Hu, C.1    Shu, C.-W.2
  • 54
    • 34547135890 scopus 로고    scopus 로고
    • Shu C-W. Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. In: Cockburn B, Johnson C, Shu C-W, Tadmor E, Quarteroni A, editors. Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, Lecture notes in mathematics, vol. 1697. Berlin: Springer; 1998. p. 325-432.
  • 55
    • 0001328401 scopus 로고
    • Calculation of interaction of non-steady shock waves with obstacles
    • Rusanov V.V. Calculation of interaction of non-steady shock waves with obstacles. J Comput Math Phys USSR 1 (1961) 261-279
    • (1961) J Comput Math Phys USSR , vol.1 , pp. 261-279
    • Rusanov, V.V.1
  • 56
    • 2942757053 scopus 로고
    • Approximate Riemann solvers, parameter vectors, and difference schemes
    • Roe P.L. Approximate Riemann solvers, parameter vectors, and difference schemes. J Comput Phys 43 (1981) 357-372
    • (1981) J Comput Phys , vol.43 , pp. 357-372
    • Roe, P.L.1
  • 57
    • 0000104186 scopus 로고    scopus 로고
    • Mass flux schemes and connection to shock instability
    • Liou M.-S. Mass flux schemes and connection to shock instability. J Comput Phys 160 (2000) 623-648
    • (2000) J Comput Phys , vol.160 , pp. 623-648
    • Liou, M.-S.1
  • 58
    • 84954695021 scopus 로고
    • Analysis and design of numerical schemes for gas dynamics. I. Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence
    • Jameson A. Analysis and design of numerical schemes for gas dynamics. I. Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence. Int J Comput Fluid Dyn 4 (1994) 171-218
    • (1994) Int J Comput Fluid Dyn , vol.4 , pp. 171-218
    • Jameson, A.1
  • 59
    • 34547092126 scopus 로고    scopus 로고
    • Delanaye M, Liu Y. Quadratic reconstruction finite volume schemes on 3D arbitrary unstructured polyhedral grids. AIAA Paper No. 99-3259-CP, 1999.
  • 60
    • 48749139407 scopus 로고
    • The numerical simulation of two-dimensional fluid flow with strong shocks
    • Woodward P., and Colella P. The numerical simulation of two-dimensional fluid flow with strong shocks. J Comput Phys 54 (1984) 115
    • (1984) J Comput Phys , vol.54 , pp. 115
    • Woodward, P.1    Colella, P.2
  • 62
    • 0034499923 scopus 로고    scopus 로고
    • Fast block lower-upper symmetric Gauss Seidel scheme for arbitrary grids
    • Chen R.F., and Wang Z.J. Fast block lower-upper symmetric Gauss Seidel scheme for arbitrary grids. AIAA J 38 12 (2000) 2238-2245
    • (2000) AIAA J , vol.38 , Issue.12 , pp. 2238-2245
    • Chen, R.F.1    Wang, Z.J.2
  • 64
    • 34547113956 scopus 로고    scopus 로고
    • Solin P, Segeth K, Dolezel I. Higher-order finite element methods, London, Boca Raton: Chapman & Hall, CRC; 2004.
  • 67
    • 34547132751 scopus 로고    scopus 로고
    • Gerritsma M, De Maerschalck B. The least squares spectral element method CFD-higher order discretization methods. In: Deconinck H, Ricchiuto M, editors. von Karman Institute for Fluid Dynamics; 2006.
  • 68
    • 34547127087 scopus 로고    scopus 로고
    • Bonhaus DL. A high-order accurate finite element method for viscous compressible flow, AIAA Paper No. 99-0780, 1999.
  • 69
    • 34547092373 scopus 로고    scopus 로고
    • Venkatakrishnan V, Allmaras SR, Kamenetski DS, Johnson FT. Higher order schemes for the compressible Navier-Stokes equations. AIAA Paper No. 2003-3987, 2003.
  • 70
    • 34447651479 scopus 로고    scopus 로고
    • Reed WH, Hill TR. Triangular mesh methods for the neutron transport equation. Technical Report LA-UR-73-479, Los Alamos Scientific Laboratory; 1973.
  • 71
    • 45249130080 scopus 로고
    • TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one-dimensional systems
    • Cockburn B., Lin S.-Y., and Shu C.-W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one-dimensional systems. J Comput Phys 84 (1989) 90-113
    • (1989) J Comput Phys , vol.84 , pp. 90-113
    • Cockburn, B.1    Lin, S.-Y.2    Shu, C.-W.3
  • 72
    • 84966261380 scopus 로고
    • TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: the multidimensional case
    • Cockburn B., Hou S., and Shu C.-W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: the multidimensional case. Math Comput 54 (1990) 545-581
    • (1990) Math Comput , vol.54 , pp. 545-581
    • Cockburn, B.1    Hou, S.2    Shu, C.-W.3
  • 73
    • 0001690553 scopus 로고    scopus 로고
    • The Runge-Kutta discontinuous Galerkin finite element method for conservation laws V: multidimensional systems
    • Cockburn B., and Shu C.-W. The Runge-Kutta discontinuous Galerkin finite element method for conservation laws V: multidimensional systems. J Comput Phys 141 (1998) 199-224
    • (1998) J Comput Phys , vol.141 , pp. 199-224
    • Cockburn, B.1    Shu, C.-W.2
  • 74
    • 0031537299 scopus 로고    scopus 로고
    • High-order accurate discontinuous finite element solution of the 2D Euler equations
    • Bassi F., and Rebay S. High-order accurate discontinuous finite element solution of the 2D Euler equations. J Comput Phys 138 (1997) 251-285
    • (1997) J Comput Phys , vol.138 , pp. 251-285
    • Bassi, F.1    Rebay, S.2
  • 75
    • 0001416032 scopus 로고    scopus 로고
    • A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
    • Bassi F., and Rebay S. A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. J Comput Phys 131 1 (1997) 267-279
    • (1997) J Comput Phys , vol.131 , Issue.1 , pp. 267-279
    • Bassi, F.1    Rebay, S.2
  • 76
    • 0037056468 scopus 로고    scopus 로고
    • Numerical evaluation of two discontinuous Galerkin methods for the compressible Navier-Stokes equations
    • Bassi F., and Rebay S. Numerical evaluation of two discontinuous Galerkin methods for the compressible Navier-Stokes equations. Int J Numer Methods Fluids 40 1 (2002) 197-207
    • (2002) Int J Numer Methods Fluids , vol.40 , Issue.1 , pp. 197-207
    • Bassi, F.1    Rebay, S.2
  • 77
    • 0000653923 scopus 로고    scopus 로고
    • Quadrature-free implementation of discontinuous Galerkin method for hyperbolic equations
    • Atkin H.L., and Shu C.-W. Quadrature-free implementation of discontinuous Galerkin method for hyperbolic equations. AIAA J 36 (1998) 775-782
    • (1998) AIAA J , vol.36 , pp. 775-782
    • Atkin, H.L.1    Shu, C.-W.2
  • 78
    • 0032720726 scopus 로고    scopus 로고
    • A discontinuous hp finite element method for the Euler and Navier-Stokes equations
    • Baumann C.E., and Oden T.J. A discontinuous hp finite element method for the Euler and Navier-Stokes equations. Int J Numer Methods Fluids 31 1 (1999) 79-95
    • (1999) Int J Numer Methods Fluids , vol.31 , Issue.1 , pp. 79-95
    • Baumann, C.E.1    Oden, T.J.2
  • 79
    • 3843100623 scopus 로고    scopus 로고
    • On the discontinuous Galerkin method for the numerical solution of the Navier-Stokes equations
    • Doleji V. On the discontinuous Galerkin method for the numerical solution of the Navier-Stokes equations. Int J Numer Methods Fluids 45 10 (2004) 1083-1106
    • (2004) Int J Numer Methods Fluids , vol.45 , Issue.10 , pp. 1083-1106
    • Doleji, V.1
  • 80
    • 34547100724 scopus 로고    scopus 로고
    • Huynh HT. An upwind moment scheme for conservation laws. in: Groth, Zingg, editors. Proceedings of the third international conference of CFD, Toronto, Canada, 2004.
  • 81
    • 26944450512 scopus 로고    scopus 로고
    • High-order accurate implementation of solid wall boundary conditions in curved geometries
    • Krivodonova L., and Berger M. High-order accurate implementation of solid wall boundary conditions in curved geometries. J Comput Phys 211 2 (2006) 492-512
    • (2006) J Comput Phys , vol.211 , Issue.2 , pp. 492-512
    • Krivodonova, L.1    Berger, M.2
  • 82
    • 0027698783 scopus 로고
    • Discontinuous Galerkin finite element method for Euler and Navier-Stokes equations
    • Lin S.Y., and Chin Y.S. Discontinuous Galerkin finite element method for Euler and Navier-Stokes equations. AIAA J 31 11 (1993) 2016-2026
    • (1993) AIAA J , vol.31 , Issue.11 , pp. 2016-2026
    • Lin, S.Y.1    Chin, Y.S.2
  • 83
    • 0033558751 scopus 로고    scopus 로고
    • A discontinuous Galerkin method for the Navier-Stokes equations
    • Lomtev I., and Karniadakis G.E. A discontinuous Galerkin method for the Navier-Stokes equations. Int J Numer Methods Fluids 29 5 (1999) 587-603
    • (1999) Int J Numer Methods Fluids , vol.29 , Issue.5 , pp. 587-603
    • Lomtev, I.1    Karniadakis, G.E.2
  • 84
    • 34547092628 scopus 로고    scopus 로고
    • Lowrie, RB, Roe PL, van Leer B. A space-time discontinuous Galerkin method for the time accurate numerical solution of hyperbolic conservation laws. AIAA Paper No. 95-1658, 1995.
  • 85
    • 0346421322 scopus 로고    scopus 로고
    • A discontinuous Galerkin method/HLLC solver for the Euler equations
    • Remaki M., and Habashi W.G. A discontinuous Galerkin method/HLLC solver for the Euler equations. Int J Numer Methods Fluids 43 12 (2003) 1391-1405
    • (2003) Int J Numer Methods Fluids , vol.43 , Issue.12 , pp. 1391-1405
    • Remaki, M.1    Habashi, W.G.2
  • 86
    • 0036865807 scopus 로고    scopus 로고
    • Space time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows: I. General formulation
    • Van der Vegt J.J.W., and Van der Ven H. Space time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows: I. General formulation. J Comput Phys 182 2 (2002) 546-585
    • (2002) J Comput Phys , vol.182 , Issue.2 , pp. 546-585
    • Van der Vegt, J.J.W.1    Van der Ven, H.2
  • 87
    • 0002084927 scopus 로고    scopus 로고
    • The development of discontinuous Galerkin methods
    • Cockburn B., Karniadakis G.E., and Shu C.W. (Eds), Springer, Berlin
    • Cockburn B., Karniadakis G.E., and Shu C.W. The development of discontinuous Galerkin methods. In: Cockburn B., Karniadakis G.E., and Shu C.W. (Eds). Discontinuous Galerkin methods (2000), Springer, Berlin
    • (2000) Discontinuous Galerkin methods
    • Cockburn, B.1    Karniadakis, G.E.2    Shu, C.W.3
  • 88
    • 0036410391 scopus 로고    scopus 로고
    • Arnold, DN, Brezzi, F, Cockburn, B, Marin LD. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J Numer Anal 2001;39:1749-79.
  • 89
    • 0032209437 scopus 로고    scopus 로고
    • A discontinuous hp finite element method for diffusion problems
    • Oden J.T., Babuska I., and Baumann C.E. A discontinuous hp finite element method for diffusion problems. J Comput Phys 146 2 (1998) 491-519
    • (1998) J Comput Phys , vol.146 , Issue.2 , pp. 491-519
    • Oden, J.T.1    Babuska, I.2    Baumann, C.E.3
  • 90
    • 0344393366 scopus 로고    scopus 로고
    • The local discontinuous Galerkin method for time-dependent convection diffusion system
    • Cockburn B., and Shu C.-W. The local discontinuous Galerkin method for time-dependent convection diffusion system. SIAM J Numer Anal 35 (1998) 2440-2463
    • (1998) SIAM J Numer Anal , vol.35 , pp. 2440-2463
    • Cockburn, B.1    Shu, C.-W.2
  • 91
    • 34547136402 scopus 로고    scopus 로고
    • Harris R, Wang ZJ, Liu Y. Efficient implementation of high-order spectral volume method for multidimensional conservation laws on unstructured grids. AIAA Paper No. 2007-912, 2007.
  • 92
    • 84966251037 scopus 로고
    • TVB uniformly high-order schemes for conservation laws
    • Shu C.-W. TVB uniformly high-order schemes for conservation laws. Math Comput 49 (1987) 105-121
    • (1987) Math Comput , vol.49 , pp. 105-121
    • Shu, C.-W.1
  • 93
    • 11144319330 scopus 로고    scopus 로고
    • Discontinuous Galerkin solutions of the Reynolds-averaged Navier-Stokes and K2o turbulence model equations
    • Bassi F., Crivellini A., Rebay S., and Savini M. Discontinuous Galerkin solutions of the Reynolds-averaged Navier-Stokes and K2o turbulence model equations. Comput Fluids 34 4-5 (2005) 507-540
    • (2005) Comput Fluids , vol.34 , Issue.4-5 , pp. 507-540
    • Bassi, F.1    Crivellini, A.2    Rebay, S.3    Savini, M.4
  • 94
    • 34547111766 scopus 로고    scopus 로고
    • Nguyen NC, Persson P-O, Peraire J. RANS solutions using high-order discontinuous Galerkin methods. AIAA Paper No. 2007-0914, 2007.
  • 95
    • 34547096931 scopus 로고    scopus 로고
    • Roe PL. Optimum upwind advection on a triangular mesh. ICASE Report 90-75, 1990.
  • 96
    • 34547108065 scopus 로고    scopus 로고
    • Deconinck H, Struijs R, Bourgeois G, Roe PL. Compact advection schemes on unstructured meshes. VKI Lecture Series 1993-04. Comput Fluid Dyn 1993.
  • 97
    • 34547109052 scopus 로고    scopus 로고
    • Paillere H, Deconinck H, Struijs R, Roe PL, Mesaros LM, Muller JD. Computations of compressible flows using fluctuation splitting on triangular meshes. AIAA Paper No. 93-3301-CP, 1993.
  • 98
    • 34547116616 scopus 로고    scopus 로고
    • Paillere H, Deconinck H, van der Weide E. Upwind residual distribution methods for compressible flow: an alternative to finite volume and finite element methods. Presented at 28th CFD VKI lecture series; 1997.
  • 100
    • 34547123520 scopus 로고    scopus 로고
    • Nishikawa H. Higher order discretization of diffusion terms in residual distribution methods. In: Deconinck H, Ricchiuto M, editors. CFD-higher order discretization methods. von Karman Institute for Fluid Dynamics; 2006.
  • 101
    • 11144279860 scopus 로고    scopus 로고
    • Compact third-order multidimensional upwind discretization for steady and unsteady flow simulations
    • Caraeni D., and Fuchs L. Compact third-order multidimensional upwind discretization for steady and unsteady flow simulations. Comput Fluids 34 (2005) 419-441
    • (2005) Comput Fluids , vol.34 , pp. 419-441
    • Caraeni, D.1    Fuchs, L.2
  • 102
    • 11144290604 scopus 로고    scopus 로고
    • A residual-based compact scheme for the unsteady compressible Navier-Stokes equations
    • Corre C., Hanss G., and Lerat A. A residual-based compact scheme for the unsteady compressible Navier-Stokes equations. Comput Fluids 34 4-5 (2005) 561-580
    • (2005) Comput Fluids , vol.34 , Issue.4-5 , pp. 561-580
    • Corre, C.1    Hanss, G.2    Lerat, A.3
  • 103
    • 0346009127 scopus 로고    scopus 로고
    • High-order fluctuation splitting schemes on triangular mesh
    • Abgrall R., and Roe P.L. High-order fluctuation splitting schemes on triangular mesh. J Sci Comput 19 (2003) 3-36
    • (2003) J Sci Comput , vol.19 , pp. 3-36
    • Abgrall, R.1    Roe, P.L.2
  • 104
    • 20344399861 scopus 로고    scopus 로고
    • Residual distribution for general time-dependent conservation laws
    • Ricchiuto M., Csik A., and Deconinck H. Residual distribution for general time-dependent conservation laws. J Comput Phys 209 (2005) 249-289
    • (2005) J Comput Phys , vol.209 , pp. 249-289
    • Ricchiuto, M.1    Csik, A.2    Deconinck, H.3
  • 105
    • 33744815230 scopus 로고    scopus 로고
    • Residual distribution schemes: current status and future trends
    • Abgrall R. Residual distribution schemes: current status and future trends. Comput Fluids 35 (2006) 641-669
    • (2006) Comput Fluids , vol.35 , pp. 641-669
    • Abgrall, R.1
  • 106
    • 0347300259 scopus 로고    scopus 로고
    • Spectral (finite) volume method for conservation laws on unstructured grids III: one-dimensional systems and partition optimization
    • Wang Z.J., and Liu Y. Spectral (finite) volume method for conservation laws on unstructured grids III: one-dimensional systems and partition optimization. J Sci Comput 20 (2004) 137-157
    • (2004) J Sci Comput , vol.20 , pp. 137-157
    • Wang, Z.J.1    Liu, Y.2
  • 107
    • 1442307691 scopus 로고    scopus 로고
    • Spectral finite volume method for conservation laws on unstructured grids IV: extension to two-dimensional systems
    • Wang Z.J., Zhang L., and Liu Y. Spectral finite volume method for conservation laws on unstructured grids IV: extension to two-dimensional systems. J Comput Phys 194 2 (2004) 716-741
    • (2004) J Comput Phys , vol.194 , Issue.2 , pp. 716-741
    • Wang, Z.J.1    Zhang, L.2    Liu, Y.3
  • 108
    • 29144498690 scopus 로고    scopus 로고
    • Spectral (finite) volume method for conservation laws on unstructured grids V: extension to three-dimensional systems
    • Liu Y., Vinokur M., and Wang Z.J. Spectral (finite) volume method for conservation laws on unstructured grids V: extension to three-dimensional systems. J Comput Phys 212 (2006) 454-472
    • (2006) J Comput Phys , vol.212 , pp. 454-472
    • Liu, Y.1    Vinokur, M.2    Wang, Z.J.3
  • 109
    • 33645850107 scopus 로고    scopus 로고
    • Spectral (finite) volume method for conservation laws on unstructured grids VI: extension to viscous flow
    • Sun Y., Wang Z.J., and Liu Y. Spectral (finite) volume method for conservation laws on unstructured grids VI: extension to viscous flow. J Comput Phys 215 1 (2006) 41-58
    • (2006) J Comput Phys , vol.215 , Issue.1 , pp. 41-58
    • Sun, Y.1    Wang, Z.J.2    Liu, Y.3
  • 110
    • 33746052067 scopus 로고    scopus 로고
    • Partitions of a simplex leading to accurate spectral (finite) volume reconstruction
    • Chen Q.-Y. Partitions of a simplex leading to accurate spectral (finite) volume reconstruction. SIAM J Sci Comput 27 4 (2006) 1458-1470
    • (2006) SIAM J Sci Comput , vol.27 , Issue.4 , pp. 1458-1470
    • Chen, Q.-Y.1
  • 111
    • 33845497697 scopus 로고    scopus 로고
    • Partitions for spectral finite volume reconstruction in the tetrahedron
    • Chen Q.Y. Partitions for spectral finite volume reconstruction in the tetrahedron. J Sci Comput 29 3 (2006) 299-319
    • (2006) J Sci Comput , vol.29 , Issue.3 , pp. 299-319
    • Chen, Q.Y.1
  • 112
    • 3142602902 scopus 로고    scopus 로고
    • Evaluation of discontinuous Galerkin and spectral volume methods for scalar and system conservation laws on unstructured grid
    • Sun Y., and Wang Z.J. Evaluation of discontinuous Galerkin and spectral volume methods for scalar and system conservation laws on unstructured grid. Int J Numer Methods Fluids 45 8 (2004) 819-838
    • (2004) Int J Numer Methods Fluids , vol.45 , Issue.8 , pp. 819-838
    • Sun, Y.1    Wang, Z.J.2
  • 113
    • 11144343214 scopus 로고    scopus 로고
    • An analysis and a comparison between the discontinuous Galerkin method and the spectral finite volume methods
    • Zhang M., and Shu C.W. An analysis and a comparison between the discontinuous Galerkin method and the spectral finite volume methods. Comput Fluids 34 4-5 (2005) 581-592
    • (2005) Comput Fluids , vol.34 , Issue.4-5 , pp. 581-592
    • Zhang, M.1    Shu, C.W.2
  • 114
    • 34547098792 scopus 로고    scopus 로고
    • Haga T, Ohnishi N, Sawada K, Masunaga A. Spectral volume computation of flowfield in aerospace application using earth simulator. AIAA Paper No. 2006-2823, 2006.
  • 115
    • 34248590309 scopus 로고    scopus 로고
    • Van den Abeele K, Broeckhoven T, Lacor C. Dispersion and dissipation properties of the 1D spectral volume method and application to a p-multigrid algorithm. J Comput Phys 2007;224:616-36.
  • 116
    • 34547117322 scopus 로고    scopus 로고
    • Van den Abeele K, Lacor C. An accuracy and stability study of the 2D spectral volume method. J. Comput Phys, in press.
  • 117
    • 34547122836 scopus 로고    scopus 로고
    • Liu Y, Vinokur M, Wang ZJ. Discontinuous spectral difference method for conservation laws on unstructured grids. In: Proceedings of the 3rd international conference on computational fluid dynamics, Toronto, Canada, July 12-16, 2004.
  • 118
    • 33646897364 scopus 로고    scopus 로고
    • Discontinuous spectral difference method for conservation laws on unstructured grids
    • Liu Y., Vinokur M., and Wang Z.J. Discontinuous spectral difference method for conservation laws on unstructured grids. J Comput Phys 216 (2006) 780-801
    • (2006) J Comput Phys , vol.216 , pp. 780-801
    • Liu, Y.1    Vinokur, M.2    Wang, Z.J.3
  • 119
    • 84884972203 scopus 로고    scopus 로고
    • Wang ZJ, Liu Y. The spectral difference method for the 2D Euler equations on unstructured grids. AIAA Paper No. 2005-5112, 2005.
  • 120
    • 34250893230 scopus 로고    scopus 로고
    • Wang ZJ, Liu Y, May G, Jameson A. Spectral difference method for unstructured grids II: extension to the Euler equations. J Sci Comput 2007;32:45-71.
  • 121
    • 34547136148 scopus 로고    scopus 로고
    • May G, Jameson A. A spectral difference method for the Euler and Navier-Stokes equations. AIAA Paper No. 2006-304, 2006.
  • 122
    • 34547119245 scopus 로고    scopus 로고
    • Wang ZJ, Sun Y, Liang C, Liu Y. Extension of the SD method to viscous flow on unstructured grids. In: Proceedings of the 4th international conference on computational fluid dynamics, Gent, Belgium, July 2006.
  • 123
    • 34547137345 scopus 로고    scopus 로고
    • May G, Jameson A. High-order accurate methods for high-speed flow. AIAA Paper No. 2005-5251, 2005.
  • 124
    • 84884936204 scopus 로고    scopus 로고
    • Huang PG, Wang ZJ, Liu Y. An implicit space-time spectral difference method for discontinuity capturing using adaptive polynomials. AIAA-2005-5255, 2005.
  • 125
    • 0030118562 scopus 로고    scopus 로고
    • A conservative staggered-grid Chebyshev multidomain method for compressible flows
    • Kopriva D.A., and Kolias J.H. A conservative staggered-grid Chebyshev multidomain method for compressible flows. J Comput Phys 125 (1996) 244
    • (1996) J Comput Phys , vol.125 , pp. 244
    • Kopriva, D.A.1    Kolias, J.H.2
  • 126
    • 0009919336 scopus 로고    scopus 로고
    • Exact integration of polynomials and symmetric quadrature formulas over arbitrary polygonal grids
    • Liu Y., and Vinokur M. Exact integration of polynomials and symmetric quadrature formulas over arbitrary polygonal grids. J Comput Phys 140 1 (1998) 122-1247
    • (1998) J Comput Phys , vol.140 , Issue.1 , pp. 122-1247
    • Liu, Y.1    Vinokur, M.2
  • 127
    • 0000185847 scopus 로고    scopus 로고
    • From electrostatics to almost optimal nodal sets for polynomial interpolation in a simplex
    • Hesthaven J.S. From electrostatics to almost optimal nodal sets for polynomial interpolation in a simplex. SIAM J Numer Anal 35 2 (1998) 655-676
    • (1998) SIAM J Numer Anal , vol.35 , Issue.2 , pp. 655-676
    • Hesthaven, J.S.1
  • 128
    • 85150403756 scopus 로고    scopus 로고
    • Sun Y, Wang ZJ, Liu Y. High-order multidomain spectral difference method for the Navier-Stokes equations on unstructured hexahedral grids. Commun Comput Phys 2007;2:310-33.
  • 129
    • 34547138626 scopus 로고    scopus 로고
    • Jameson A, Schmidt W, Turkel E. Numerical solution of the Euler equations by finite volume methods using Runge-Kutta time stepping schemes. AIAA Paper No. 81-1259; 1981.
  • 130
    • 0344047770 scopus 로고
    • Solution of the Euler equations by a multigrid method
    • Jameson A. Solution of the Euler equations by a multigrid method. Appl Math Comput 13 (1983) 327-356
    • (1983) Appl Math Comput , vol.13 , pp. 327-356
    • Jameson, A.1
  • 131
    • 0000564951 scopus 로고
    • Total-variation-diminishing time discretizations
    • Shu C.-W. Total-variation-diminishing time discretizations. SIAM J Sci Stat Comput 9 (1988) 1073-1084
    • (1988) SIAM J Sci Stat Comput , vol.9 , pp. 1073-1084
    • Shu, C.-W.1
  • 132
    • 45449125925 scopus 로고
    • Efficient implementation of essentially non-oscillatory shock-capturing schemes
    • Shu C.-W., and Osher S. Efficient implementation of essentially non-oscillatory shock-capturing schemes. J Comput Phys 77 (1988) 439-471
    • (1988) J Comput Phys , vol.77 , pp. 439-471
    • Shu, C.-W.1    Osher, S.2
  • 133
    • 0032345207 scopus 로고    scopus 로고
    • Total variation diminishing Runge-Kutta schemes
    • Gottlieb S., and Shu C.W. Total variation diminishing Runge-Kutta schemes. Math Comput 67 (1998) 73-85
    • (1998) Math Comput , vol.67 , pp. 73-85
    • Gottlieb, S.1    Shu, C.W.2
  • 134
    • 0001118530 scopus 로고    scopus 로고
    • A new class of optimal high-order strong-stability preserving time discretization methods
    • Spiteri R.J., and Ruuth S.J. A new class of optimal high-order strong-stability preserving time discretization methods. SIAM J Numer Anal 40 (2002) 469-491
    • (2002) SIAM J Numer Anal , vol.40 , pp. 469-491
    • Spiteri, R.J.1    Ruuth, S.J.2
  • 135
    • 28844507125 scopus 로고    scopus 로고
    • On high-order strong stability preserving Runge-Kutta and multi step time discretizations
    • Gottlieb S. On high-order strong stability preserving Runge-Kutta and multi step time discretizations. J Sci Comput 25 1/2 (2005) 105-128
    • (2005) J Sci Comput , vol.25 , Issue.1-2 , pp. 105-128
    • Gottlieb, S.1
  • 136
    • 28144432137 scopus 로고
    • Implicit solvers for unstructured meshes
    • Venkatakrishnan V., and Mavriplis D.J. Implicit solvers for unstructured meshes. J Comput Phys 105 1 (1993) 83-91
    • (1993) J Comput Phys , vol.105 , Issue.1 , pp. 83-91
    • Venkatakrishnan, V.1    Mavriplis, D.J.2
  • 137
    • 0000048673 scopus 로고
    • GMRES: A genearlized minimal residual algorithm for solving nonsymmetric linear systems
    • Saad Y., and Schultz M.H. GMRES: A genearlized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7 (1986) 865
    • (1986) SIAM J Sci Stat Comput , vol.7 , pp. 865
    • Saad, Y.1    Schultz, M.H.2
  • 138
    • 0035922223 scopus 로고    scopus 로고
    • An efficient implicit discontinuous Galerkin method
    • Rasetarinera P., and Hussaini M.Y. An efficient implicit discontinuous Galerkin method. J Comput Phys 172 2 (2001) 718-738
    • (2001) J Comput Phys , vol.172 , Issue.2 , pp. 718-738
    • Rasetarinera, P.1    Hussaini, M.Y.2
  • 139
    • 84982318784 scopus 로고    scopus 로고
    • Sharov D, Nakahashi K. Low speed preconditioning and LUSGS scheme for 3D viscous flow computations on unstructured grids. AIAA Paper No. 98-0614, January 1998.
  • 140
    • 0000841777 scopus 로고    scopus 로고
    • Multigrid strategies for viscous flow solvers on anisotropic unstructured meshes
    • Mavriplis D.J. Multigrid strategies for viscous flow solvers on anisotropic unstructured meshes. J Comput Phys 145 (1998) 141-165
    • (1998) J Comput Phys , vol.145 , pp. 141-165
    • Mavriplis, D.J.1
  • 141
    • 31744436751 scopus 로고    scopus 로고
    • High-order discontinuous Galerkin methods using an hp-multigrid approach
    • Nastase C.R., and Mavriplis D.J. High-order discontinuous Galerkin methods using an hp-multigrid approach. J Comput Phys 213 (2006) 330-357
    • (2006) J Comput Phys , vol.213 , pp. 330-357
    • Nastase, C.R.1    Mavriplis, D.J.2
  • 142
    • 0024070893 scopus 로고
    • Lower-upper symmetric-Gauss-Seidel method for the Euler and Navier-Stokes equations
    • Yoon S., and Jameson A. Lower-upper symmetric-Gauss-Seidel method for the Euler and Navier-Stokes equations. AIAA Journal 26 (1988) 1025-1026
    • (1988) AIAA Journal , vol.26 , pp. 1025-1026
    • Yoon, S.1    Jameson, A.2
  • 143
    • 34547136642 scopus 로고    scopus 로고
    • Soetrisno M, Imlay ST, Roberts DW. A zonal implicit procedure for hybrid structured-unstructured grids. AIAA Paper No. 94-0617, 1994.
  • 144
    • 85086490897 scopus 로고    scopus 로고
    • Jameson A, Caughey DA. How many steps are required to solve the Euler equations of steady compressible flow: in search of a fast solution algorithm. In: 15th AIAA computational fluid dynamics conference, Anaheim, CA, June 2001.
  • 145
    • 34547122681 scopus 로고    scopus 로고
    • Sun Y, Wang ZJ, Liu Y, Chen CL. Efficient implicit LU-SGS algorithm for high-order spectral difference method on unstructured hexahedral grids. AIAA Paper No. 2007-0313, 2007.
  • 146
    • 18344378961 scopus 로고    scopus 로고
    • p-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations
    • Fidkowski K.J., Oliver T.A., Lu J., and Darmofal D.L. p-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations. J Comput Phys 207 (2005) 92-113
    • (2005) J Comput Phys , vol.207 , pp. 92-113
    • Fidkowski, K.J.1    Oliver, T.A.2    Lu, J.3    Darmofal, D.L.4
  • 147
    • 34547096932 scopus 로고    scopus 로고
    • Allmaras S. Analysis of semi-implicit preconditioners for multigrid solution of the 2-D Navier Stokes equations. AIAA Paper 95-1651, AIAA 12th computational fluid dynamics conference, San Diego, CA, June 1995.
  • 148
    • 34547119244 scopus 로고    scopus 로고
    • Alonso JJ, Martinelli L, Jameson A. Multigrid unsteady Navier Stokes calculations with aeroelastic applications. AIAA Paper 95-0048, AIAA 33rd aerospace sciences meeting, Reno, NV, January 1995.
  • 149
    • 34547095943 scopus 로고    scopus 로고
    • Hemker PW, Koren B. Defect correction and non-linear multi-grid for the steady Euler equations. Lecture Notes, 1988-05 von Karman Institute for Fluid Dynamics, 1988.
  • 150
    • 0025474529 scopus 로고
    • Multigrid solution of the Navier-Stokes equations on triangular meshes
    • Mavriplis D.J., and Jameson A. Multigrid solution of the Navier-Stokes equations on triangular meshes. AIAA J 28 (1990) 1415-1425
    • (1990) AIAA J , vol.28 , pp. 1415-1425
    • Mavriplis, D.J.1    Jameson, A.2
  • 151
    • 0002249736 scopus 로고
    • A high-resolution Euler solver based on multigrid, semi-coarsening, and defect correction
    • Mulder W.A. A high-resolution Euler solver based on multigrid, semi-coarsening, and defect correction. J Comput Phys 100 (1992) 91-104
    • (1992) J Comput Phys , vol.100 , pp. 91-104
    • Mulder, W.A.1
  • 152
    • 45949116154 scopus 로고
    • Preconditioned methods for solving the incompressible and low speed compressible equations
    • Turkel E. Preconditioned methods for solving the incompressible and low speed compressible equations. J Comput Phys 72 (1987) 277
    • (1987) J Comput Phys , vol.72 , pp. 277
    • Turkel, E.1
  • 153
    • 28144434245 scopus 로고
    • The application of preconditioning in viscous flows
    • Choi Y.H., and Merkle C.L. The application of preconditioning in viscous flows. J Comput Phys 105 2 (1993) 207-223
    • (1993) J Comput Phys , vol.105 , Issue.2 , pp. 207-223
    • Choi, Y.H.1    Merkle, C.L.2
  • 154
    • 84962161019 scopus 로고    scopus 로고
    • Van Leer B, Lee WT, Roe PL. Characteristic time-stepping or local preconditioning of the Euler equations. AIAA Paper No. 91-1552; 1991.
  • 155
    • 0000784858 scopus 로고
    • Spectral element multigrid I: formulation and numerical results
    • Ronquist E.M., and Patera A.T. Spectral element multigrid I: formulation and numerical results. SIAM J Sci Comput 2 4 (1987) 389-406
    • (1987) SIAM J Sci Comput , vol.2 , Issue.4 , pp. 389-406
    • Ronquist, E.M.1    Patera, A.T.2
  • 156
    • 34547130014 scopus 로고    scopus 로고
    • Maday Y, Munoz R. Spectral element multigrid part 2: theoretical justification. ICASE, Technical Report 1988; 88-73.
  • 157
    • 34547113954 scopus 로고    scopus 로고
    • Bassi F, Rebay S. Numerical solution of the Euler equations with a multiorder discontinuous finite element method. In: Proceedings of the second international conference on computational fluid dynamics, Sydney, Australia, 15-19 July 2002.
  • 158
    • 2942732331 scopus 로고    scopus 로고
    • Helenbrook B, Mavriplis D, Atkins H. Analysis of p-multigrid for continuous and discontinuous finite element discretizations. AIAA Paper 2003-3989, AIAA, 2003.
  • 159
    • 26944434674 scopus 로고    scopus 로고
    • A p-multigrid discontinuous Galerkin method for the Euler equations on unstructured grids
    • Luo H., Baum J.D., and Lohner R. A p-multigrid discontinuous Galerkin method for the Euler equations on unstructured grids. J Comput Phys 211 (2006) 767-783
    • (2006) J Comput Phys , vol.211 , pp. 767-783
    • Luo, H.1    Baum, J.D.2    Lohner, R.3
  • 161
    • 0035281653 scopus 로고    scopus 로고
    • Spectral methods for hyperbolic problems
    • Gottlieb D., and Hesthaven J. Spectral methods for hyperbolic problems. J Comput Appl Math 128 (2001) 83-131
    • (2001) J Comput Appl Math , vol.128 , pp. 83-131
    • Gottlieb, D.1    Hesthaven, J.2
  • 162
    • 34547136403 scopus 로고    scopus 로고
    • Harten A, Chakravarthy S. Multi-dimensional ENO Schemes for general geometries, ICASE Report No. 91-76; 1991.
  • 164
    • 0022477699 scopus 로고
    • Characteristic-based schemes for the Euler equations
    • Roe P.L. Characteristic-based schemes for the Euler equations. Annu Rev Fluid Mech 18 (1986) 337-365
    • (1986) Annu Rev Fluid Mech , vol.18 , pp. 337-365
    • Roe, P.L.1
  • 165
    • 0020223604 scopus 로고    scopus 로고
    • Van Leer B. Flux-vector splitting for the Euler equations. Lecture notes in physics, 1982; vol. 170. p. 507.
  • 166
    • 34547105501 scopus 로고    scopus 로고
    • Vassberg JC. A fast, implicit unstructured-mesh Euler method. AIAA Paper No. 92-2693, 1992.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.