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Volumn 226, Issue 1, 2007, Pages 204-243

Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems

Author keywords

ADER approach; Nonlinear hyperbolic systems; Quadrature free finite volume schemes; Unstructured meshes in 2D and 3D; WENO reconstruction

Indexed keywords

IMAGE RECONSTRUCTION;

EID: 34548397128     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.04.004     Document Type: Article
Times cited : (340)

References (58)
  • 1
    • 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. Journal of Computational Physics 144 (1994) 45-58
    • (1994) Journal of Computational Physics , vol.144 , pp. 45-58
    • Abgrall, R.1
  • 2
    • 0000653923 scopus 로고    scopus 로고
    • Quadrature-free implementation of the discontinuous Galerkin method for hyperbolic equations
    • Atkins H., and Shu C.W. Quadrature-free implementation of the discontinuous Galerkin method for hyperbolic equations. AIAA Journal 36 (1998) 775-782
    • (1998) AIAA Journal , vol.36 , pp. 775-782
    • Atkins, H.1    Shu, C.W.2
  • 3
    • 0000897959 scopus 로고    scopus 로고
    • Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy
    • Balsara D., and Shu C.W. Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy. Journal of Computational Physics 160 (2000) 405-452
    • (2000) Journal of Computational Physics , vol.160 , pp. 405-452
    • Balsara, D.1    Shu, C.W.2
  • 4
    • 85189848759 scopus 로고    scopus 로고
    • T.J. Barth, P.O. Frederickson, Higher order solution of the Euler equations on unstructured grids using quadratic reconstruction. AIAA paper no. 90-0013, 28th Aerospace Sciences Meeting January 1990.
  • 5
    • 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. Journal of Computational Physics 138 (1997) 251-285
    • (1997) Journal of Computational Physics , vol.138 , pp. 251-285
    • Bassi, F.1    Rebay, S.2
  • 6
    • 48349083249 scopus 로고
    • A second-order Godunov-type scheme for compressible fluid dynamics
    • Ben-Artzi M., and Falcovitz J. A second-order Godunov-type scheme for compressible fluid dynamics. Journal of Computational Physics 55 (1984) 1-32
    • (1984) Journal of Computational Physics , vol.55 , pp. 1-32
    • Ben-Artzi, M.1    Falcovitz, J.2
  • 7
    • 0040686631 scopus 로고
    • An asymptotic expansion for the solution of the generalized riemann problem. Part II: application to the gas dynamics equations
    • Bourgeade A., LeFloch P., and Raviart P.A. An asymptotic expansion for the solution of the generalized riemann problem. Part II: application to the gas dynamics equations. Annales de l'institut Henri Poincaré (C) Analyse non linéaire 6 (1989) 437-480
    • (1989) Annales de l'institut Henri Poincaré (C) Analyse non linéaire , vol.6 , pp. 437-480
    • Bourgeade, A.1    LeFloch, P.2    Raviart, P.A.3
  • 8
    • 85189846664 scopus 로고    scopus 로고
    • G. Chiocchia, Exact solutions to transonic and supersonic flows. AGARD Advisory Report AR-211, 1985.
  • 9
    • 84966261380 scopus 로고
    • The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: the multidimensional case
    • Cockburn B., Hou S., and Shu C.W. The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: the multidimensional case. Mathematics of Computation 54 (1990) 545-581
    • (1990) Mathematics of Computation , vol.54 , pp. 545-581
    • Cockburn, B.1    Hou, S.2    Shu, C.W.3
  • 11
    • 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. Journal of Computational Physics 84 (1989) 90-113
    • (1989) Journal of Computational Physics , vol.84 , pp. 90-113
    • Cockburn, B.1    Lin, S.Y.2    Shu, C.W.3
  • 12
    • 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. Mathematics of Computation 52 (1989) 411-435
    • (1989) Mathematics of Computation , vol.52 , pp. 411-435
    • Cockburn, B.1    Shu, C.W.2
  • 13
    • 0000869912 scopus 로고
    • The Runge-Kutta local projection P1-Discontinuous Galerkin finite element method for scalar conservation laws
    • Cockburn B., and Shu C.W. The Runge-Kutta local projection P1-Discontinuous Galerkin finite element method for scalar conservation laws. Mathematical Modelling and Numerical Analysis 25 (1991) 337-361
    • (1991) Mathematical Modelling and Numerical Analysis , vol.25 , pp. 337-361
    • Cockburn, B.1    Shu, C.W.2
  • 14
    • 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. Journal of Computational Physics 141 (1998) 199-224
    • (1998) Journal of Computational Physics , vol.141 , pp. 199-224
    • Cockburn, B.1    Shu, C.W.2
  • 15
    • 0026371189 scopus 로고
    • Spectral methods on triangles and other domains
    • Dubiner M. Spectral methods on triangles and other domains. Journal of Scientific Computing 6 (1991) 345-390
    • (1991) Journal of Scientific Computing , vol.6 , pp. 345-390
    • Dubiner, M.1
  • 16
    • 85189851252 scopus 로고    scopus 로고
    • M. Dumbser, M. Käser, J. de la Puente, Arbitrary high-order finite volume schemes for seismic wave propagation on unstructured meshes in two and three space dimensions, Geophysical Journal International, in press.
  • 17
    • 33846336138 scopus 로고    scopus 로고
    • Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems
    • Dumbser M., and Käser M. Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems. Journal of Computational Physics 221 (2007) 693-723
    • (2007) Journal of Computational Physics , vol.221 , pp. 693-723
    • Dumbser, M.1    Käser, M.2
  • 18
    • 85189852203 scopus 로고    scopus 로고
    • M. Dumbser, M. Käser, E.F. Toro, An arbitrary high order discontinuous Galerkin method for elastic waves on unstructured meshes V: Local time stepping and p-adaptivity, Geophysical Journal International, in press.
  • 20
    • 85189850730 scopus 로고    scopus 로고
    • M. Dumbser, C.D. Munz, On source terms and boundary conditions using arbitrary high order discontinuous Galerkin schemes, International Journal of Applied Mathematics and Scientific Computing, in press.
  • 21
    • 33745038766 scopus 로고    scopus 로고
    • Building blocks for arbitrary high order discontinuous Galerkin schemes
    • Dumbser M., and Munz C.D. Building blocks for arbitrary high order discontinuous Galerkin schemes. Journal of Scientific Computing 27 (2006) 215-230
    • (2006) Journal of Scientific Computing , vol.27 , pp. 215-230
    • Dumbser, M.1    Munz, C.D.2
  • 22
    • 85189846703 scopus 로고    scopus 로고
    • R.W. Dyson, Technique for very high order nonlinear simulation and validation. Technical Report TM-2001-210985, NASA, 2001.
  • 25
    • 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. Journal of Computational Physics 144 (1998) 194-212
    • (1998) Journal of Computational Physics , vol.144 , pp. 194-212
    • Friedrich, O.1
  • 26
    • 0000935266 scopus 로고
    • Finite difference methods for the computation of discontinuous solutions of the equations of fluid dynamics
    • Godunov S.K. Finite difference methods for the computation of discontinuous solutions of the equations of fluid dynamics. Mat. Sb. 47 (1959) 271-306
    • (1959) Mat. Sb. , vol.47 , pp. 271-306
    • Godunov, S.K.1
  • 29
    • 0000876320 scopus 로고
    • On upstream differencing and Godunov-type schemes for hyperbolic conservation laws
    • Harten A., Lax P.D., and van Leer B. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Review 25 1 (1983) 35-61
    • (1983) SIAM Review , vol.25 , Issue.1 , pp. 35-61
    • Harten, A.1    Lax, P.D.2    van Leer, B.3
  • 30
    • 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. Journal of Computational Physics 150 (1999) 97-127
    • (1999) Journal of Computational Physics , vol.150 , pp. 97-127
    • Hu, C.1    Shu, C.W.2
  • 32
    • 0002806618 scopus 로고    scopus 로고
    • Multilevel k-way partitioning scheme for irregular graphs
    • Karypis G., and Kumar V. Multilevel k-way partitioning scheme for irregular graphs. J. Parallel Distrib. Comput. 48 (1998) 96-129
    • (1998) J. Parallel Distrib. Comput. , vol.48 , pp. 96-129
    • Karypis, G.1    Kumar, V.2
  • 33
    • 17144370650 scopus 로고    scopus 로고
    • ADER schemes on adaptive triangular meshes for scalar conservation laws
    • Käser M., and Iske A. ADER schemes on adaptive triangular meshes for scalar conservation laws. Journal of Computational Physics 205 (2005) 486-508
    • (2005) Journal of Computational Physics , vol.205 , pp. 486-508
    • Käser, M.1    Iske, A.2
  • 34
    • 84980078953 scopus 로고
    • Weak solutions of nonlinear hyperbolic equations and their numerical approximation
    • Lax P.D. Weak solutions of nonlinear hyperbolic equations and their numerical approximation. Comm. Pure Appl. Math. 7 (1954) 159-193
    • (1954) Comm. Pure Appl. Math. , vol.7 , pp. 159-193
    • Lax, P.D.1
  • 35
    • 85189852398 scopus 로고    scopus 로고
    • F. Loercher, G. Gassner, C.D. Munz, A discontinuous Galerkin scheme based on a space-time expansion. i. inviscid compressible flow in one space dimension, Journal of Scientific Computing, in press.
  • 37
    • 0037144941 scopus 로고    scopus 로고
    • A high-order-accurate unstructured mesh finite-volume scheme for the advection-diffusion equation
    • Ollivier-Gooch C., and Van Altena M. A high-order-accurate unstructured mesh finite-volume scheme for the advection-diffusion equation. Journal of Computational Physics 181 (2002) 729-752
    • (2002) Journal of Computational Physics , vol.181 , pp. 729-752
    • Ollivier-Gooch, C.1    Van Altena, M.2
  • 39
    • 2942757053 scopus 로고
    • Approximate Riemann solvers, parameter vectors, and difference schemes
    • Roe P.L. Approximate Riemann solvers, parameter vectors, and difference schemes. Journal of Computational Physics 43 (1981) 357-372
    • (1981) Journal of Computational Physics , vol.43 , pp. 357-372
    • Roe, P.L.1
  • 40
    • 85189849301 scopus 로고    scopus 로고
    • H. Schardin, in: Proc. VII Int. Cong. High Speed Photg., Darmstadt, O. Helwich Verlag, 1965, pp. 113-119.
  • 41
    • 0036151484 scopus 로고    scopus 로고
    • A technique of treating negative weights in WENO schemes
    • Shi J., Hu C., and Shu C.W. A technique of treating negative weights in WENO schemes. Journal of Computational Physics 175 (2002) 108-127
    • (2002) Journal of Computational Physics , vol.175 , pp. 108-127
    • Shi, J.1    Hu, C.2    Shu, C.W.3
  • 42
    • 0001568854 scopus 로고
    • Efficient implementation of essentially non-oscillatory shock capturing schemes II
    • Shu C.W., and Osher S. Efficient implementation of essentially non-oscillatory shock capturing schemes II. Journal of Computational Physics 83 (1989) 32-78
    • (1989) Journal of Computational Physics , vol.83 , pp. 32-78
    • Shu, C.W.1    Osher, S.2
  • 43
    • 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. Computer methods in applied mechanics and engineering 140 (1997) 157-181
    • (1997) Computer methods in applied mechanics and engineering , vol.140 , pp. 157-181
    • Sonar, T.1
  • 45
    • 0031234473 scopus 로고    scopus 로고
    • Accurate monotonicity-preserving schemes with Runge-Kutta time stepping
    • Suresh A., and Huynh H.T. Accurate monotonicity-preserving schemes with Runge-Kutta time stepping. Journal of Computational Physics 136 (1997) 83-99
    • (1997) Journal of Computational Physics , vol.136 , pp. 83-99
    • Suresh, A.1    Huynh, H.T.2
  • 46
    • 33947386249 scopus 로고    scopus 로고
    • Arbitrary high order discontinuous Galerkin schemes for the magnetohydrodynamic equations
    • Taube A., Dumbser M., Balsara D., and Munz C.-D. Arbitrary high order discontinuous Galerkin schemes for the magnetohydrodynamic equations. Journal of Scientific Computing 30 (2007) 441-464
    • (2007) Journal of Scientific Computing , vol.30 , pp. 441-464
    • Taube, A.1    Dumbser, M.2    Balsara, D.3    Munz, C.-D.4
  • 47
    • 15944366192 scopus 로고    scopus 로고
    • ADER schemes for three-dimensional nonlinear hyperbolic systems
    • Titarev V.A., and Toro E.F. ADER schemes for three-dimensional nonlinear hyperbolic systems. Journal of Computational Physics 204 (2005) 715-736
    • (2005) Journal of Computational Physics , vol.204 , pp. 715-736
    • Titarev, V.A.1    Toro, E.F.2
  • 49
    • 0042072022 scopus 로고    scopus 로고
    • Towards very high order Godunov schemes
    • Godunov Methods. Toro E.F. (Ed), Kluwer/Plenum Academic Publishers
    • Toro E.F., Millington R.C., and Nejad L.A.M. Towards very high order Godunov schemes. In: Toro E.F. (Ed). Godunov Methods. Theory and Applications (2001), Kluwer/Plenum Academic Publishers 905-938
    • (2001) Theory and Applications , pp. 905-938
    • Toro, E.F.1    Millington, R.C.2    Nejad, L.A.M.3
  • 50
    • 0003122153 scopus 로고
    • Restoration of the contact surface in the Harten-Lax-van Leer Riemann solver
    • Toro E.F., Spruce M., and Speares W. Restoration of the contact surface in the Harten-Lax-van Leer Riemann solver. Journal of Shock Waves 4 (1994) 25-34
    • (1994) Journal of Shock Waves , vol.4 , pp. 25-34
    • Toro, E.F.1    Spruce, M.2    Speares, W.3
  • 51
    • 57249099681 scopus 로고    scopus 로고
    • Solution of the generalized Riemann problem for advection-reaction equations
    • Toro E.F., and Titarev V.A. Solution of the generalized Riemann problem for advection-reaction equations. Proc. Roy. Soc. London (2002) 271-281
    • (2002) Proc. Roy. Soc. London , pp. 271-281
    • Toro, E.F.1    Titarev, V.A.2
  • 52
    • 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. Journal of Computational Physics 182 (2002) 546-585
    • (2002) Journal of Computational Physics , vol.182 , pp. 546-585
    • van der Vegt, J.J.W.1    van der Ven, H.2
  • 53
    • 0037073024 scopus 로고    scopus 로고
    • Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows II. efficient flux quadrature
    • van der Ven H., and van der Vegt J.J.W. Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows II. efficient flux quadrature. Comput. Methods Appl. Mech. Engrg. 191 (2002) 4747-4780
    • (2002) Comput. Methods Appl. Mech. Engrg. , vol.191 , pp. 4747-4780
    • van der Ven, H.1    van der Vegt, J.J.W.2
  • 55
    • 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. Journal of Computational Physics 14 (1974) 361-370
    • (1974) Journal of Computational Physics , vol.14 , pp. 361-370
    • van Leer, B.1
  • 56
    • 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. Journal of Computational Physics 32 (1979) 101-136
    • (1979) Journal of Computational Physics , vol.32 , pp. 101-136
    • van Leer, B.1
  • 57
    • 25444507957 scopus 로고    scopus 로고
    • Extension of the spectral volume method to high-order boundary representation
    • Wang Z.J., and Liu Y. Extension of the spectral volume method to high-order boundary representation. Journal of Computational Physics 211 (2006) 154-178
    • (2006) Journal of Computational Physics , vol.211 , pp. 154-178
    • Wang, Z.J.1    Liu, Y.2
  • 58
    • 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. Journal of Computational Physics 54 (1984) 115-173
    • (1984) Journal of Computational Physics , vol.54 , pp. 115-173
    • Woodward, P.1    Colella, P.2


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