메뉴 건너뛰기




Volumn 228, Issue 21, 2009, Pages 8161-8186

A unifying lifting collocation penalty formulation including the discontinuous Galerkin, spectral volume/difference methods for conservation laws on mixed grids

Author keywords

Collocation; Discontinuous Galerkin; Euler equations; Finite difference; High order methods; Spectral difference; Spectral volume; Unstructured grids

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; PHYSICAL PROPERTIES;

EID: 69949151364     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.07.036     Document Type: Article
Times cited : (418)

References (54)
  • 1
    • 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
  • 3
    • 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
  • 4
    • 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
  • 5
    • 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
  • 6
    • 0002267573 scopus 로고
    • A finite volume high-order ENO scheme for two-dimensional hyperbolic systems
    • Casper J., and Atkins H.L. A finite volume high-order ENO scheme for two-dimensional hyperbolic systems. J. Comput. Phys. 106 (1993) 62-76
    • (1993) J. Comput. Phys. , vol.106 , pp. 62-76
    • Casper, J.1    Atkins, H.L.2
  • 7
    • 0029511833 scopus 로고
    • Approximate optimal points for polynomial interpolation of real functions in an interval and in a triangle
    • Chen Q., and Babuska I. Approximate optimal points for polynomial interpolation of real functions in an interval and in a triangle. Comput. Methods Appl. Mech. Eng. 128 (1995) 405-417
    • (1995) Comput. Methods Appl. Mech. Eng. , vol.128 , pp. 405-417
    • Chen, Q.1    Babuska, I.2
  • 8
    • 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
  • 9
    • 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
  • 10
    • 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
  • 11
    • 0001690553 scopus 로고    scopus 로고
    • The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems
    • Cockburn B., and Shu C.-W. The Runge-Kutta discontinuous Galerkin 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
  • 13
    • 22844446543 scopus 로고    scopus 로고
    • High-order accurate, low numerical diffusion methods for aerodynamics
    • Ekaterinaris J.A. High-order accurate, low numerical diffusion methods for aerodynamics. Prog. Aerosp. Sci. 41 (2005) 192-300
    • (2005) Prog. Aerosp. Sci. , vol.41 , pp. 192-300
    • Ekaterinaris, J.A.1
  • 14
    • 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
  • 16
    • 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
  • 17
    • 37249066633 scopus 로고    scopus 로고
    • Efficient quadrature-free high-order spectral volume method on unstructured grids: theory and 2D implementation
    • Harris R., Wang Z.J., and Liu Y. Efficient quadrature-free high-order spectral volume method on unstructured grids: theory and 2D implementation. J. Comput. Phys. 227 3 (2008) 1620-1642
    • (2008) J. Comput. Phys. , vol.227 , Issue.3 , pp. 1620-1642
    • Harris, R.1    Wang, Z.J.2    Liu, Y.3
  • 18
    • 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
  • 19
    • 0032681315 scopus 로고    scopus 로고
    • Stable spectral methods for conservation laws on triangles with unstructured grids
    • Hesthaven J.S., and Gottlieb D. Stable spectral methods for conservation laws on triangles with unstructured grids. Comput. Methods Appl. Mech. Eng. 175 (1999) 361-381
    • (1999) Comput. Methods Appl. Mech. Eng. , vol.175 , pp. 361-381
    • Hesthaven, J.S.1    Gottlieb, D.2
  • 21
    • 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
  • 23
    • 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
  • 25
    • 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
  • 26
    • 33644550669 scopus 로고    scopus 로고
    • A sequel to AUSM, Part II: AUSM+-up for all speeds
    • Liou M.-S. A sequel to AUSM, Part II: AUSM+-up for all speeds. J. Comput. Phys. 214 (2006) 137-170
    • (2006) J. Comput. Phys. , vol.214 , pp. 137-170
    • Liou, M.-S.1
  • 28
    • 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
  • 29
    • 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
  • 30
    • 54149102536 scopus 로고    scopus 로고
    • A spectral difference method for the Euler and Navier-Stokes equations
    • G. May, A. Jameson, A spectral difference method for the Euler and Navier-Stokes equations, AIAA Paper No. 2006-304, 2006.
    • (2006) AIAA Paper No , vol.2006 -304
    • May, G.1    Jameson, A.2
  • 31
    • 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
  • 32
    • 38049050745 scopus 로고    scopus 로고
    • A high-order accurate unstructured finite volume Newton-Krylov algorithm for inviscid compressible flows
    • Nejata A., and Ollivier-Gooch C. A high-order accurate unstructured finite volume Newton-Krylov algorithm for inviscid compressible flows. J. Comput. Phys. 227 (2008) 2582-2609
    • (2008) J. Comput. Phys. , vol.227 , pp. 2582-2609
    • Nejata, A.1    Ollivier-Gooch, C.2
  • 33
    • 0021413939 scopus 로고
    • Riemann solvers, the entropy condition, and difference approximations
    • Osher S. Riemann solvers, the entropy condition, and difference approximations. SIAM J. Numer. Anal. 21 (1984) 217-235
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 217-235
    • Osher, S.1
  • 35
    • 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
  • 36
    • 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
  • 37
    • 0000034725 scopus 로고    scopus 로고
    • Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws
    • Advanced Numerical Approximation of Nonlinear Hyperbolic Equations. Cockburn B., Johnson C., Shu C.-W., and Tadmor E. (Eds). Quarteroni A. (Ed), Springer
    • Shu C.-W. Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. In: Cockburn B., Johnson C., Shu C.-W., and Tadmor E. (Eds). Advanced Numerical Approximation of Nonlinear Hyperbolic Equations. In: Quarteroni A. (Ed). Lecture Notes in Mathematics vol. 1697 (1998), Springer 325-432
    • (1998) Lecture Notes in Mathematics , vol.1697 , pp. 325-432
    • Shu, C.-W.1
  • 38
    • 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
  • 40
    • 34248590309 scopus 로고    scopus 로고
    • Dispersion and dissipation properties of the 1D spectral volume method and application to a p-multigrid algorithm
    • Van den Abeele K., Broeckhoven T., and Lacor C. Dispersion and dissipation properties of the 1D spectral volume method and application to a p-multigrid algorithm. J. Comput. Phys. 224 2 (2007) 616-636
    • (2007) J. Comput. Phys. , vol.224 , Issue.2 , pp. 616-636
    • Van den Abeele, K.1    Broeckhoven, T.2    Lacor, C.3
  • 41
    • 34548429140 scopus 로고    scopus 로고
    • An accuracy and stability study of the 2D spectral volume method
    • Van den Abeele K., and Lacor C. An accuracy and stability study of the 2D spectral volume method. J. Comput. Phys. 226 1 (2007) 1007-1026
    • (2007) J. Comput. Phys. , vol.226 , Issue.1 , pp. 1007-1026
    • Van den Abeele, K.1    Lacor, C.2
  • 42
    • 54149107259 scopus 로고    scopus 로고
    • On the stability and accuracy of the spectral difference method
    • Van den Abeele K., Lacor C., and Wang Z.J. On the stability and accuracy of the spectral difference method. J. Sci. Comput. 37 2 (2008) 162-188
    • (2008) J. Sci. Comput. , vol.37 , Issue.2 , pp. 162-188
    • Van den Abeele, K.1    Lacor, C.2    Wang, Z.J.3
  • 43
    • 36148968111 scopus 로고    scopus 로고
    • On the connection between the spectral volume and the spectral difference method
    • Abeele K.V.d., Lacor C., and Wang Z.J. On the connection between the spectral volume and the spectral difference method. J. Comput. Phys. 227 2 (2007) 877-885
    • (2007) J. Comput. Phys. , vol.227 , Issue.2 , pp. 877-885
    • Abeele, K.V.d.1    Lacor, C.2    Wang, Z.J.3
  • 44
    • 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
  • 45
    • 84884972630 scopus 로고    scopus 로고
    • Discontinuous Galerkin for diffusion
    • B. Van Leer, S. Nomura, Discontinuous Galerkin for diffusion, AIAA Paper No. 2005-5108, 2005.
    • (2005) AIAA Paper No , Issue.2005-5108
    • Van Leer, B.1    Nomura, S.2
  • 47
    • 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
  • 48
    • 34547093896 scopus 로고    scopus 로고
    • High-order methods for the Euler and Navier-Stokes equations on unstructured grids
    • Wang Z.J. High-order methods for the Euler and Navier-Stokes equations on unstructured grids. J. Prog. Aerosp. Sci. 43 (2007) 1-47
    • (2007) J. Prog. Aerosp. Sci. , vol.43 , pp. 1-47
    • Wang, Z.J.1
  • 49
    • 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 (2002) 665-697
    • (2002) J. Comput. Phys. , vol.179 , pp. 665-697
    • Wang, Z.J.1    Liu, Y.2
  • 50
    • 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 1 (2004) 137-157
    • (2004) J. Sci. Comput. , vol.20 , Issue.1 , pp. 137-157
    • Wang, Z.J.1    Liu, Y.2
  • 51
    • 1442307691 scopus 로고    scopus 로고
    • Spectral (finite) volume method for conservation laws on unstructured grids IV: extension to two-dimensional Euler equations
    • Wang Z.J., Zhang L., and Liu Y. Spectral (finite) volume method for conservation laws on unstructured grids IV: extension to two-dimensional Euler equations. 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
  • 52
    • 33846667672 scopus 로고    scopus 로고
    • An explicit construction of interpolation nodes on the simplex
    • Warburton T. An explicit construction of interpolation nodes on the simplex. J. Eng. Math. 56 (2006) 247-262
    • (2006) J. Eng. Math. , vol.56 , pp. 247-262
    • Warburton, T.1
  • 53
    • 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 J. 26 (1988) 1025-1026
    • (1988) AIAA J. , vol.26 , pp. 1025-1026
    • Yoon, S.1    Jameson, A.2
  • 54
    • 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


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.