메뉴 건너뛰기




Volumn 227, Issue 8, 2008, Pages 3971-4001

Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws

Author keywords

ADER approach; Finite volume schemes; Hyperbolic balance laws; Local space time discontinuous Galerkin method; Stiff source terms; WENO reconstruction

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; CONVERGENCE OF NUMERICAL METHODS; EULER EQUATIONS; FRICTION; PHYSICAL PROPERTIES;

EID: 40249111500     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.12.005     Document Type: Article
Times cited : (294)

References (66)
  • 1
    • 0036894036 scopus 로고    scopus 로고
    • Error estimates on the random projection methods for hyperbolic conservation laws with stiff reaction terms
    • W. Bao S. Jin Error estimates on the random projection methods for hyperbolic conservation laws with stiff reaction terms Applied Numerical Mathematics 43 2002 315 333
    • (2002) Applied Numerical Mathematics , vol.43 , pp. 315-333
    • Bao, W.1    Jin, S.2
  • 2
    • 0030158716 scopus 로고    scopus 로고
    • Zero-relaxation limit versus operator splitting for two-phase fluid flow computations
    • F. Béreux Zero-relaxation limit versus operator splitting for two-phase fluid flow computations Computer Methods in Applied Mechanics and Engineering 133 1996 93 124
    • (1996) Computer Methods in Applied Mechanics and Engineering , vol.133 , pp. 93-124
    • Béreux, F.1
  • 3
    • 0028534347 scopus 로고
    • Upwind methods for hyperbolic conservation laws with source terms
    • A. Bermudez M.E. Vazquez Upwind methods for hyperbolic conservation laws with source terms Computers and Fluids 23 8 1994 1049 1071
    • (1994) Computers and Fluids , vol.23 , Issue.8 , pp. 1049-1071
    • Bermudez, A.1    Vazquez, M.E.2
  • 4
    • 85009821047 scopus 로고    scopus 로고
    • Equilibrium schemes for scalar conservation laws with stiff sources
    • R. Botchorishvili B. Perthame A. Vasseur Equilibrium schemes for scalar conservation laws with stiff sources Mathematics of Computation 72 241 2001 131 157
    • (2001) Mathematics of Computation , vol.72 , Issue.241 , pp. 131-157
    • Botchorishvili, R.1    Perthame, B.2    Vasseur, A.3
  • 7
    • 0026142448 scopus 로고
    • One-dimensional front tracking based on high resolution wave propagation methods
    • A. Bourlioux A.J. Majda V. Roytburd One-dimensional front tracking based on high resolution wave propagation methods SIAM Journal on Applied Mathematics 51 1991 303 343
    • (1991) SIAM Journal on Applied Mathematics , vol.51 , pp. 303-343
    • Bourlioux, A.1    Majda, A.J.2    Roytburd, V.3
  • 8
    • 33846453345 scopus 로고    scopus 로고
    • Asymptotic preserving and positive schemes for radiation hydrodynamics
    • C. Buet B. Després Asymptotic preserving and positive schemes for radiation hydrodynamics Journal of Computational Physics 215 2 2006 717 740
    • (2006) Journal of Computational Physics , vol.215 , Issue.2 , pp. 717-740
    • Buet, C.1    Després, B.2
  • 9
    • 0029412755 scopus 로고
    • Numerical analysis of two operator splitting methods for an hyperbolic system of conservation laws with stiff relaxation
    • E. Burman L. Sainsaulieu Numerical analysis of two operator splitting methods for an hyperbolic system of conservation laws with stiff relaxation Computer Methods in Applied Mechanics and Engineering 128 1995 291 314
    • (1995) Computer Methods in Applied Mechanics and Engineering , vol.128 , pp. 291-314
    • Burman, E.1    Sainsaulieu, L.2
  • 10
    • 0001407297 scopus 로고    scopus 로고
    • Uniformly accurate schemes for hyperbolic systems with relaxation
    • R.E. Caflish S. Jin G. Russo Uniformly accurate schemes for hyperbolic systems with relaxation SIAM Journal on Numerical Analysis 34 1997 246 281
    • (1997) SIAM Journal on Numerical Analysis , vol.34 , pp. 246-281
    • Caflish, R.E.1    Jin, S.2    Russo, G.3
  • 11
    • 33746371365 scopus 로고    scopus 로고
    • High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products, applications to shallow-water systems
    • M. Castro J.M. Gallardo C. Pares High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products, applications to shallow-water systems Mathematics of Computation 75 2006 1103 1134
    • (2006) Mathematics of Computation , vol.75 , pp. 1103-1134
    • Castro, M.1    Gallardo, J.M.2    Pares, C.3
  • 13
    • 33745031784 scopus 로고    scopus 로고
    • Arbitrary High Order Schemes for the Solution of Hyperbolic Conservation Laws in Complex Domains
    • M. Dumbser Arbitrary High Order Schemes for the Solution of Hyperbolic Conservation Laws in Complex Domains 2005 Shaker Verlag Aachen
    • (2005)
    • Dumbser, M.1
  • 14
    • 33846336138 scopus 로고    scopus 로고
    • Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems
    • M. Dumbser M. Käser 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
  • 15
    • 34548397128 scopus 로고    scopus 로고
    • Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems
    • M. Dumbser M. Käser V.A. Titarev E.F. Toro Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems Journal of Computational Physics 226 2007 204 243
    • (2007) Journal of Computational Physics , vol.226 , pp. 204-243
    • Dumbser, M.1    Käser, M.2    Titarev, V.A.3    Toro, E.F.4
  • 16
    • 33745038766 scopus 로고    scopus 로고
    • Building blocks for arbitrary high order discontinuous Galerkin schemes
    • M. Dumbser C.D. Munz 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
  • 17
    • 33845458104 scopus 로고    scopus 로고
    • Arbitrary high order finite volume schemes for linear wave propagation
    • M. Dumbser T. Schwartzkopff C.D. Munz Arbitrary high order finite volume schemes for linear wave propagation Computational Science and High Performance Computing II Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM) 2006 Springer-Verlag Berlin, Heidelberg 129 144
    • (2006) , pp. 129-144
    • Dumbser, M.1    Schwartzkopff, T.2    Munz, C.D.3
  • 20
    • 84966208277 scopus 로고
    • One sided difference approximations for nonlinear conservation laws
    • B. Engquist S. Osher One sided difference approximations for nonlinear conservation laws Mathematics of Computation 36 1981 321 351
    • (1981) Mathematics of Computation , vol.36 , pp. 321-351
    • Engquist, B.1    Osher, S.2
  • 21
  • 22
    • 0000935266 scopus 로고
    • Finite difference methods for the computation of discontinuous solutions of the equations of fluid dynamics
    • S.K. Godunov Finite difference methods for the computation of discontinuous solutions of the equations of fluid dynamics Mathematics of the USSR. Sbornik 47 1959 271 306
    • (1959) Mathematics of the USSR. Sbornik , vol.47 , pp. 271-306
    • Godunov, S.K.1
  • 23
    • 0000804338 scopus 로고    scopus 로고
    • The convergence of numerical transfer schemes in diffusive regimes. I: The discrete-ordinate method
    • F. Golse S. Jin C.D. Levermore The convergence of numerical transfer schemes in diffusive regimes. I: The discrete-ordinate method SIAM Journal on Numerical Analysis 36 1999 1333 1369
    • (1999) SIAM Journal on Numerical Analysis , vol.36 , pp. 1333-1369
    • Golse, F.1    Jin, S.2    Levermore, C.D.3
  • 24
    • 0034209981 scopus 로고    scopus 로고
    • A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms
    • L. Gosse A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms Computers and Mathematics with Applications 39 2000 135 159
    • (2000) Computers and Mathematics with Applications , vol.39 , pp. 135-159
    • Gosse, L.1
  • 25
    • 4544386272 scopus 로고    scopus 로고
    • Asymptotic-preserving and well-balanced schemes for radiative transfer and the Rosseland approximation
    • L. Gosse G. Toscani Asymptotic-preserving and well-balanced schemes for radiative transfer and the Rosseland approximation Numerische Mathematik 98 2 2004 223 250
    • (2004) Numerische Mathematik , vol.98 , Issue.2 , pp. 223-250
    • Gosse, L.1    Toscani, G.2
  • 26
    • 1542576141 scopus 로고    scopus 로고
    • A well-balanced scheme for the numerical processing of source terms in hyperbolic equations
    • J.M. Greenberg A.Y. LeRoux A well-balanced scheme for the numerical processing of source terms in hyperbolic equations SIAM Journal on Numerical Analysis 33 1 1996 1 16
    • (1996) SIAM Journal on Numerical Analysis , vol.33 , Issue.1 , pp. 1-16
    • Greenberg, J.M.1    LeRoux, A.Y.2
  • 28
    • 0000876320 scopus 로고
    • On upstream differencing and Godunov-type schemes for hyperbolic conservation laws
    • A. Harten P.D. Lax B. van Leer 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
  • 29
    • 0034879512 scopus 로고    scopus 로고
    • Modified fractional step method for the accurate approximation of detonation waves
    • C. Helzel R.J. LeVeque G. Warnecke Modified fractional step method for the accurate approximation of detonation waves SIAM Journal on Scientific Computing 22 2000 1489 1510
    • (2000) SIAM Journal on Scientific Computing , vol.22 , pp. 1489-1510
    • Helzel, C.1    LeVeque, R.J.2    Warnecke, G.3
  • 30
    • 0000580833 scopus 로고
    • Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping
    • L. Hsiao T.P. Liu Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping Communications in Mathematical Physics 143 1992 599 605
    • (1992) Communications in Mathematical Physics , vol.143 , pp. 599-605
    • Hsiao, L.1    Liu, T.P.2
  • 31
    • 17444396696 scopus 로고    scopus 로고
    • Convergence to the Barenblatt solution for the compressible Euler equations with damping and vacuum
    • F. Huang P. Marcati R. Pan Convergence to the Barenblatt solution for the compressible Euler equations with damping and vacuum Archive for Rational Mechanics and Analysis 176 2005 1 24
    • (2005) Archive for Rational Mechanics and Analysis , vol.176 , pp. 1-24
    • Huang, F.1    Marcati, P.2    Pan, R.3
  • 33
    • 0001862602 scopus 로고
    • Runge–Kutta methods for hyperbolic conservation laws with stiff relaxation terms
    • S. Jin Runge–Kutta methods for hyperbolic conservation laws with stiff relaxation terms Journal of Computational Physics 122 1 1995 51 67
    • (1995) Journal of Computational Physics , vol.122 , Issue.1 , pp. 51-67
    • Jin, S.1
  • 34
    • 0033295423 scopus 로고    scopus 로고
    • Efficient asymptotic-preserving (ap) schemes for some multiscale kinetic equations
    • S. Jin Efficient asymptotic-preserving (ap) schemes for some multiscale kinetic equations SIAM Journal on Scientific Computing 21 1999 441 454
    • (1999) SIAM Journal on Scientific Computing , vol.21 , pp. 441-454
    • Jin, S.1
  • 35
    • 0035537697 scopus 로고    scopus 로고
    • A steady-state capturing method for hyperbolic systems with geometrical source terms
    • S. Jin A steady-state capturing method for hyperbolic systems with geometrical source terms Mathematical Modelling and Numerical Analysis 35 4 2001 631 645
    • (2001) Mathematical Modelling and Numerical Analysis , vol.35 , Issue.4 , pp. 631-645
    • Jin, S.1
  • 36
    • 0030194392 scopus 로고    scopus 로고
    • Numerical schemes for hyperbolic conservation laws with stiff relaxation terms
    • S. Jin C.D. Levermore Numerical schemes for hyperbolic conservation laws with stiff relaxation terms Journal of Computational Physics 126 2 1996 449 467
    • (1996) Journal of Computational Physics , vol.126 , Issue.2 , pp. 449-467
    • Jin, S.1    Levermore, C.D.2
  • 37
    • 84990701264 scopus 로고
    • The relaxation schemes for systems of conservation laws in arbitrary space dimensions
    • S. Jin Z. Xin The relaxation schemes for systems of conservation laws in arbitrary space dimensions Communications on Pure and Applied Mathematics 48 1995 235 277
    • (1995) Communications on Pure and Applied Mathematics , vol.48 , pp. 235-277
    • Jin, S.1    Xin, Z.2
  • 38
    • 0038908817 scopus 로고
    • An asymptotic expansion for the solution of the generalized Riemann problem, Part I: general theory
    • P. LeFloch P.A. Raviart An asymptotic expansion for the solution of the generalized Riemann problem, Part I: general theory Annales de l’Institut Henri Poincaré 5 2 1988 179 207
    • (1988) Annales de l’Institut Henri Poincaré , vol.5 , Issue.2 , pp. 179-207
    • LeFloch, P.1    Raviart, P.A.2
  • 39
    • 85190397596 scopus 로고    scopus 로고
    • A.Y. LeRoux, Riemann solvers for some hyperbolic problems with a source term, in: ESAIM: Proceedings CANUM, vol. 6, 1998, pp. 75–90.
  • 40
    • 0000087732 scopus 로고
    • One-dimensional front tracking based on high resolution wave propagation methods
    • R.J. LeVeque K.-M. Shyue One-dimensional front tracking based on high resolution wave propagation methods SIAM Journal on Scientific Computing 16 1995 348 377
    • (1995) SIAM Journal on Scientific Computing , vol.16 , pp. 348-377
    • LeVeque, R.J.1    Shyue, K.-M.2
  • 41
    • 0000542076 scopus 로고
    • A study of numerical methods for hyperbolic conservation laws with stiff source terms
    • R.J. LeVeque H.C. Yee A study of numerical methods for hyperbolic conservation laws with stiff source terms Journal of Computational Physics 86 1 1990 187 210
    • (1990) Journal of Computational Physics , vol.86 , Issue.1 , pp. 187-210
    • LeVeque, R.J.1    Yee, H.C.2
  • 44
    • 34248596734 scopus 로고    scopus 로고
    • A modified higher order Godunov’s scheme for stiff source conservative hydrodynamics
    • F. Miniati P. Colella A modified higher order Godunov’s scheme for stiff source conservative hydrodynamics Journal of Computational Physics 224 2 2007 519 538
    • (2007) Journal of Computational Physics , vol.224 , Issue.2 , pp. 519-538
    • Miniati, F.1    Colella, P.2
  • 45
    • 0000287554 scopus 로고    scopus 로고
    • Numerical schemes for hyperbolic systems of conservation laws with stiff diffusive relaxation
    • G. Naldi L. Pareschi Numerical schemes for hyperbolic systems of conservation laws with stiff diffusive relaxation SIAM Journal on Numerical Analysis 37 4 2000 1246 1270
    • (2000) SIAM Journal on Numerical Analysis , vol.37 , Issue.4 , pp. 1246-1270
    • Naldi, G.1    Pareschi, L.2
  • 46
    • 84968510942 scopus 로고
    • Upwind difference schemes for hyperbolic conservation laws
    • S. Osher F. Solomon Upwind difference schemes for hyperbolic conservation laws Mathematics of Computation 38 1982 339 374
    • (1982) Mathematics of Computation , vol.38 , pp. 339-374
    • Osher, S.1    Solomon, F.2
  • 47
    • 0012148580 scopus 로고    scopus 로고
    • Implicit-explicit Runge–Kutta schemes for stiff systems of differential equations
    • L. Pareschi G. Russo Implicit-explicit Runge–Kutta schemes for stiff systems of differential equations Advances in the Theory of Computational Mathematics 3 2000 269 288
    • (2000) Advances in the Theory of Computational Mathematics , vol.3 , pp. 269-288
    • Pareschi, L.1    Russo, G.2
  • 48
    • 0027677962 scopus 로고
    • Numerical methods for hyperbolic conservation laws with stiff relaxation, I. Spurious solutions
    • R.B. Pember Numerical methods for hyperbolic conservation laws with stiff relaxation, I. Spurious solutions SIAM Journal on Applied Mathematics 53 5 1993 1293 1330
    • (1993) SIAM Journal on Applied Mathematics , vol.53 , Issue.5 , pp. 1293-1330
    • Pember, R.B.1
  • 49
    • 0000417595 scopus 로고
    • Numerical methods for hyperbolic conservation laws with stiff relaxation. II. Higher order Godunov methods
    • R.B. Pember Numerical methods for hyperbolic conservation laws with stiff relaxation. II. Higher order Godunov methods SIAM Journal on Scientific Computing 14 4 1993 824 859
    • (1993) SIAM Journal on Scientific Computing , vol.14 , Issue.4 , pp. 824-859
    • Pember, R.B.1
  • 50
    • 11244301807 scopus 로고    scopus 로고
    • Convergence of the upwind interface source method for hyperbolic conservation laws
    • B. Perthame C. Simeoni Convergence of the upwind interface source method for hyperbolic conservation laws T. Hou E. Tadmor Proceedings of Hyp2002 2003 Springer
    • (2003)
    • Perthame, B.1    Simeoni, C.2
  • 53
    • 0348207606 scopus 로고    scopus 로고
    • Finite difference WENO schemes with Lax–Wendroff type time discretization
    • J. Qiu C.W. Shu Finite difference WENO schemes with Lax–Wendroff type time discretization SIAM Journal on Scientific Computing 24 6 2003 2185 2198
    • (2003) SIAM Journal on Scientific Computing , vol.24 , Issue.6 , pp. 2185-2198
    • Qiu, J.1    Shu, C.W.2
  • 54
    • 2942757053 scopus 로고
    • Approximate Riemann solvers, parameter vectors, and difference schemes
    • P.L. Roe 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
  • 56
    • 0001568854 scopus 로고
    • Efficient implementation of essentially non-oscillatory shock capturing schemes II
    • C.W. Shu S. Osher 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
  • 57
    • 0001518684 scopus 로고
    • On the construction and comparison of difference schemes
    • G. Strang On the construction and comparison of difference schemes SIAM Journal on Numerical Analysis 5 3 1968 506 517
    • (1968) SIAM Journal on Numerical Analysis , vol.5 , Issue.3 , pp. 506-517
    • Strang, G.1
  • 58
    • 0003769405 scopus 로고
    • Approximate Calculation of Multiple Integrals
    • A.H. Stroud Approximate Calculation of Multiple Integrals 1971 Prentice-Hall Inc. Englewood Cliffs, New Jersey
    • (1971)
    • Stroud, A.H.1
  • 59
    • 0008392886 scopus 로고    scopus 로고
    • ADER: arbitrary high order Godunov approach
    • V.A. Titarev E.F. Toro ADER: arbitrary high order Godunov approach Journal of Scientific Computing 17 1–4 2002 609 618 December
    • (2002) Journal of Scientific Computing , vol.17 , Issue.1–4 , pp. 609-618
    • Titarev, V.A.1    Toro, E.F.2
  • 60
    • 15944366192 scopus 로고    scopus 로고
    • ADER schemes for three-dimensional nonlinear hyperbolic systems
    • V.A. Titarev E.F. Toro 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
  • 61
    • 0003542590 scopus 로고    scopus 로고
    • Riemann Solvers and Numerical Methods for Fluid Dynamics
    • E.F. Toro Riemann Solvers and Numerical Methods for Fluid Dynamics second ed. 1999 Springer
    • (1999)
    • Toro, E.F.1
  • 62
    • 0042072022 scopus 로고    scopus 로고
    • Towards very high order Godunov schemes
    • E.F. Toro R.C. Millington L.A.M. Nejad Towards very high order Godunov schemes E.F. Toro Godunov Methods. Theory and Applications 2001 Kluwer/Plenum Academic Publishers 905 938
    • (2001) , pp. 905-938
    • Toro, E.F.1    Millington, R.C.2    Nejad, L.A.M.3
  • 63
    • 0003122153 scopus 로고
    • Restoration of the contact surface in the Harten–Lax–van Leer Riemann solver
    • E.F. Toro M. Spruce W. Speares 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
  • 65
    • 8744299687 scopus 로고    scopus 로고
    • ADER schemes for scalar hyperbolic conservation laws with source terms in three space dimensions
    • E.F. Toro V.A. Titarev ADER schemes for scalar hyperbolic conservation laws with source terms in three space dimensions Journal of Computational Physics 202 2005 196 215
    • (2005) Journal of Computational Physics , vol.202 , pp. 196-215
    • Toro, E.F.1    Titarev, V.A.2
  • 66
    • 0036865807 scopus 로고    scopus 로고
    • Space–time discontinuous Galerkin finite element method with dynamics grid motion for inviscid compressible flows, part I. General formulation
    • J. van der Vegt H. van der Ven Space–time discontinuous Galerkin finite element method with dynamics grid motion for inviscid compressible flows, part 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.1    van der Ven, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.