메뉴 건너뛰기




Volumn 228, Issue 7, 2009, Pages 2480-2516

Efficient, high accuracy ADER-WENO schemes for hydrodynamics and divergence-free magnetohydrodynamics

Author keywords

ADER; Magnetohydrodynamics; Numerical methods; Unsteady compressible flow; WENO

Indexed keywords

ASTROPHYSICS; FINITE VOLUME METHOD; GALERKIN METHODS; INTERPOLATION; MAGNETOHYDRODYNAMICS; MAGNETOPLASMA; RUNGE KUTTA METHODS;

EID: 60149101429     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.12.003     Document Type: Article
Times cited : (279)

References (60)
  • 1
    • 0032339882 scopus 로고    scopus 로고
    • Linearized formulation of the Riemann problem for adiabatic and isothermal magnetohydrodynamics
    • Balsara D.S. Linearized formulation of the Riemann problem for adiabatic and isothermal magnetohydrodynamics. Astrophysical Journal Suppl. 116 (1998) 119
    • (1998) Astrophysical Journal , Issue.SUPPL. 116 , pp. 119
    • Balsara, D.S.1
  • 2
    • 0032337254 scopus 로고    scopus 로고
    • Total variation diminishing algorithm for adiabatic and isothermal magnetohydrodynamics
    • Balsara D.S. Total variation diminishing algorithm for adiabatic and isothermal magnetohydrodynamics. Astrophysical Journal Suppl. 116 (1998) 133
    • (1998) Astrophysical Journal , Issue.SUPPL. 116 , pp. 133
    • Balsara, D.S.1
  • 3
    • 0035842859 scopus 로고    scopus 로고
    • Divergence-free adaptive mesh refinement for magnetohydrodynamics
    • Balsara D.S. Divergence-free adaptive mesh refinement for magnetohydrodynamics. Journal of Computational Physics 174 (2001) 614-648
    • (2001) Journal of Computational Physics , vol.174 , pp. 614-648
    • Balsara, D.S.1
  • 4
    • 0035628942 scopus 로고    scopus 로고
    • Total variation diminishing scheme for relativistic magneto-hydrodynamics
    • Balsara D.S. Total variation diminishing scheme for relativistic magneto-hydrodynamics. Astrophysical Journal Suppl. 132 (2001) 83
    • (2001) Astrophysical Journal , Issue.SUPPL. 132 , pp. 83
    • Balsara, D.S.1
  • 5
    • 1842764950 scopus 로고    scopus 로고
    • Second-order-accurate schemes for magnetohydrodynamics with divergence-free reconstruction
    • Balsara D.S. Second-order-accurate schemes for magnetohydrodynamics with divergence-free reconstruction. Astrophysical Journal Suppl. 151 (2004) 149-184
    • (2004) Astrophysical Journal , Issue.SUPPL. 151 , pp. 149-184
    • Balsara, D.S.1
  • 6
    • 85190073318 scopus 로고    scopus 로고
    • Divergence-free reconstruction of magnetic fields and WENO schemes for magnetohydrodynamics submitted
    • Balsara D.S. Divergence-free reconstruction of magnetic fields and WENO schemes for magnetohydrodynamics submitted. Journal of Computational Physics (2008)
    • (2008) Journal of Computational Physics
    • Balsara, D.S.1
  • 7
    • 34548438386 scopus 로고    scopus 로고
    • A sub-cell based indicator for troubled zones in RKDG schemes and a novel class oh hybrid RKDG + HWENO schemes
    • Balsara D.S., Altmann C., Munz C.D., and Dumbser M. A sub-cell based indicator for troubled zones in RKDG schemes and a novel class oh hybrid RKDG + HWENO schemes. Journal of Computational Physics 226 (2007) 586-620
    • (2007) Journal of Computational Physics , vol.226 , pp. 586-620
    • Balsara, D.S.1    Altmann, C.2    Munz, C.D.3    Dumbser, M.4
  • 8
    • 85190075179 scopus 로고    scopus 로고
    • ADER schemes for problems with stiff source terms - method and application to two-fluid magnetohydrodynamics, in preparation
    • Balsara D.S., Dumbser M., and Tilley D.A. ADER schemes for problems with stiff source terms - method and application to two-fluid magnetohydrodynamics, in preparation. Journal Computational Physics (2008)
    • (2008) Journal Computational Physics
    • Balsara, D.S.1    Dumbser, M.2    Tilley, D.A.3
  • 9
    • 0000897959 scopus 로고    scopus 로고
    • Monotonicity preserving weighted non-oscillatory schemes wirh increasingly high order of accuracy
    • Balsara D.S., and Shu C.-W. Monotonicity preserving weighted non-oscillatory schemes wirh 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.S.1    Shu, C.-W.2
  • 10
    • 0348194853 scopus 로고    scopus 로고
    • Maintaining pressure positivity in magnetohydrodynamic simulations
    • Balsara D.S., and Spicer D.S. Maintaining pressure positivity in magnetohydrodynamic simulations. Journal of Computational Physics 148 (1999) 133-148
    • (1999) Journal of Computational Physics , vol.148 , pp. 133-148
    • Balsara, D.S.1    Spicer, D.S.2
  • 11
    • 0001690874 scopus 로고    scopus 로고
    • A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations
    • Balsara D.S., and Spicer D.S. A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations. Journal of Computational Physics 149 (1999) 270-292
    • (1999) Journal of Computational Physics , vol.149 , pp. 270-292
    • Balsara, D.S.1    Spicer, D.S.2
  • 12
    • 85003456409 scopus 로고
    • Higher order solution of the Euler equations on unstructured grids using quadratic reconstruction
    • AIAA Paper no. 90-0013, January
    • 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.
    • (1990) 28th Aerospace Sciences Meeting
    • Barth, T.J.1    Frederickson, P.O.2
  • 13
    • 11744289966 scopus 로고
    • Local adaptive mesh refinement for shock hydrodynamics
    • Berger M., and Colella P. Local adaptive mesh refinement for shock hydrodynamics. Journal of Computational Physics 82 (1989) 64-84
    • (1989) Journal of Computational Physics , vol.82 , pp. 64-84
    • Berger, M.1    Colella, P.2
  • 14
    • 0001689247 scopus 로고
    • The effect of nonzero ΔB on the numerical solution of the magnetohydrodynamic equations
    • Brackbill J.U., and Barnes D.C. The effect of nonzero ΔB on the numerical solution of the magnetohydrodynamic equations. Journal of Computational Physics 35 (1980) 426-430
    • (1980) Journal of Computational Physics , vol.35 , pp. 426-430
    • Brackbill, J.U.1    Barnes, D.C.2
  • 16
    • 0001690553 scopus 로고    scopus 로고
    • The Runge-Kutta discontinuous Galerkin method for Conservation Laws V
    • Cockburn B., and Shu C.-W. The Runge-Kutta discontinuous Galerkin method for Conservation Laws V. 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
  • 17
    • 26844455510 scopus 로고
    • Multidimensional upwind methods for hyperbolic conservation laws
    • Colella P. Multidimensional upwind methods for hyperbolic conservation laws. Journal of Computational Physics 87 (1990) 171-200
    • (1990) Journal of Computational Physics , vol.87 , pp. 171-200
    • Colella, P.1
  • 18
    • 34547419627 scopus 로고
    • The piecewise parabolic method (PPM) for gas-dynamical simulations
    • Colella P., and Woodward P. The piecewise parabolic method (PPM) for gas-dynamical simulations. Journal of Computational Physics 54 (1984) 174-201
    • (1984) Journal of Computational Physics , vol.54 , pp. 174-201
    • Colella, P.1    Woodward, P.2
  • 20
    • 28144445934 scopus 로고
    • An approximate Riemann solver for ideal magnetohydrodynamics
    • Dai W., and Woodward P.R. An approximate Riemann solver for ideal magnetohydrodynamics. Journal of Computational Physics 111 (1994) 354-372
    • (1994) Journal of Computational Physics , vol.111 , pp. 354-372
    • Dai, W.1    Woodward, P.R.2
  • 21
    • 33645674549 scopus 로고    scopus 로고
    • On the divergence-free condition and conservation laws in numerical simulations for supersonic magnetohydrodynamic flows
    • Dai W., and Woodward P.R. On the divergence-free condition and conservation laws in numerical simulations for supersonic magnetohydrodynamic flows. Astrophysical Journal 494 (1998) 317-335
    • (1998) Astrophysical Journal , vol.494 , pp. 317-335
    • Dai, W.1    Woodward, P.R.2
  • 23
    • 0035242764 scopus 로고    scopus 로고
    • Parametric decay of circularly polarized Alfvén waves: multidimensional simulations in periodic and open domains
    • Del Zanna L., Velli M., and Londrillo P. Parametric decay of circularly polarized Alfvén waves: multidimensional simulations in periodic and open domains. Astronomy and Astrophysics 367 (2001) 705-718
    • (2001) Astronomy and Astrophysics , vol.367 , pp. 705-718
    • Del Zanna, L.1    Velli, M.2    Londrillo, P.3
  • 24
    • 0001409128 scopus 로고
    • Flux-corrected transport techniques for multidimensional compressible magnetohydrodynamics
    • DeVore C.R. Flux-corrected transport techniques for multidimensional compressible magnetohydrodynamics. Journal of Computational Physics 92 (1991) 142-160
    • (1991) Journal of Computational Physics , vol.92 , pp. 142-160
    • DeVore, C.R.1
  • 25
    • 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
  • 26
    • 48149096340 scopus 로고    scopus 로고
    • A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes
    • Dumbser M., Balsara D., Toro E.F., and Munz C.D. A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes. Journal of Computational Physics 227 (2008) 8209-8253
    • (2008) Journal of Computational Physics , vol.227 , pp. 8209-8253
    • Dumbser, M.1    Balsara, D.2    Toro, E.F.3    Munz, C.D.4
  • 27
    • 40249111500 scopus 로고    scopus 로고
    • Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws
    • Dumbser M., Enaux C., and Toro E.F. Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws. Journal of Computational Physics 227 (2008) 3971-4001
    • (2008) Journal of Computational Physics , vol.227 , pp. 3971-4001
    • Dumbser, M.1    Enaux, C.2    Toro, E.F.3
  • 28
    • 33846336138 scopus 로고    scopus 로고
    • Arbitary high order non-oscillatory finite volume schmes on unstuructured meshes for linear hyperbolic systems
    • Dumbser M., and Käser M. Arbitary high order non-oscillatory finite volume schmes on unstuructured meshes for linear hyperbolic systems. Journal of Computational Physcis 221 (2007) 693-723
    • (2007) Journal of Computational Physcis , vol.221 , pp. 693-723
    • Dumbser, M.1    Käser, M.2
  • 29
    • 34548397128 scopus 로고    scopus 로고
    • Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems
    • Dumbser M., Käser M., Titarev V.A., and Toro E.F. 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
  • 33
    • 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
  • 34
    • 0000770459 scopus 로고
    • An instability of finite amplitude circularly polarized Alfven waves
    • Goldstein M.L. An instability of finite amplitude circularly polarized Alfven waves. Astrophysical Journal 219 (1978) 700
    • (1978) Astrophysical Journal , vol.219 , pp. 700
    • Goldstein, M.L.1
  • 35
    • 45849110272 scopus 로고    scopus 로고
    • Improving shock irregularities based on the characteristics of the MHD equations
    • Hanawa T., Mikami H., and Matsumoto T. Improving shock irregularities based on the characteristics of the MHD equations. Journal of Computational Physics 227 (2008) 7952-7976
    • (2008) Journal of Computational Physics , vol.227 , pp. 7952-7976
    • Hanawa, T.1    Mikami, H.2    Matsumoto, T.3
  • 37
    • 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
  • 38
    • 0041805923 scopus 로고
    • On the dispersion relations for parametric instabilities of parallel-propagating Alfvén waves
    • Jayanti V., and Hollweg J.V. On the dispersion relations for parametric instabilities of parallel-propagating Alfvén waves. Journal of Geophysical Research 98 (1993) 13247-13252
    • (1993) Journal of Geophysical Research , vol.98 , pp. 13247-13252
    • Jayanti, V.1    Hollweg, J.V.2
  • 40
    • 0030161771 scopus 로고    scopus 로고
    • Efficient implementation of weighted ENO schemes
    • Jiang G.-S., and Shu C.-W. Efficient implementation of weighted ENO schemes. Journal of Computational Physics 126 (1996) 202-228
    • (1996) Journal of Computational Physics , vol.126 , pp. 202-228
    • Jiang, G.-S.1    Shu, C.-W.2
  • 41
    • 0033586043 scopus 로고    scopus 로고
    • A multidimensional code for isothermal magnetohydrodynamic flows in astrophysics
    • Kim J.S., Ryu D., Jones T.W., and Hong S.S. A multidimensional code for isothermal magnetohydrodynamic flows in astrophysics. Astrophysical Journal 514 (1999) 506-519
    • (1999) Astrophysical Journal , vol.514 , pp. 506-519
    • Kim, J.S.1    Ryu, D.2    Jones, T.W.3    Hong, S.S.4
  • 43
    • 1542531258 scopus 로고    scopus 로고
    • On the divergence-free condition in Godunov-type schemes for ideal magnetohydrodynamics: the upwind constrained transport method
    • Londrillo P., and DelZanna L. On the divergence-free condition in Godunov-type schemes for ideal magnetohydrodynamics: the upwind constrained transport method. Journal of Computational Physics 195 (2004) 17-48
    • (2004) Journal of Computational Physics , vol.195 , pp. 17-48
    • Londrillo, P.1    DelZanna, L.2
  • 44
    • 0001477246 scopus 로고    scopus 로고
    • Numerical instabilities in upwind methods: analysis and cures for the "Carbuncle" phenomenon
    • Pandolfini M., and D'Ambrosio D. Numerical instabilities in upwind methods: analysis and cures for the "Carbuncle" phenomenon. J Journal of Computational Physics 166 (2001) 271
    • (2001) J Journal of Computational Physics , vol.166 , pp. 271
    • Pandolfini, M.1    D'Ambrosio, D.2
  • 45
    • 0008104353 scopus 로고    scopus 로고
    • An approximate Riemann solver for MHD (That actually works in more than one dimension
    • 94-24
    • K.G. Powell, An approximate Riemann solver for MHD (That actually works in more than one dimension, ICASE Report 94-24.
    • ICASE Report
    • Powell, K.G.1
  • 48
    • 11944265404 scopus 로고
    • Numerical MHD in astrophysics: algorithm and tests for one-dimensional flow
    • Ryu D., and Jones T.W. Numerical MHD in astrophysics: algorithm and tests for one-dimensional flow. Astrophysical Journal 442 (1995) 228
    • (1995) Astrophysical Journal , vol.442 , pp. 228
    • Ryu, D.1    Jones, T.W.2
  • 49
    • 0012381666 scopus 로고    scopus 로고
    • A divergence-free upwind code for multidimensional magnetohydrodynamic flows
    • Ryu D., Miniati F., Jones T.W., and Frank A. A divergence-free upwind code for multidimensional magnetohydrodynamic flows. Astrophysical Journal 509 (1998) 244-255
    • (1998) Astrophysical Journal , vol.509 , pp. 244-255
    • Ryu, D.1    Miniati, F.2    Jones, T.W.3    Frank, A.4
  • 50
    • 45449125925 scopus 로고
    • Efficient implementation of essentially non-oscillatory shock capturing schemes
    • Shu C.-W., and Osher S.J. Efficient implementation of essentially non-oscillatory shock capturing schemes. Journal of Computational Physics 77 (1988) 439-471
    • (1988) Journal of Computational Physics , vol.77 , pp. 439-471
    • Shu, C.-W.1    Osher, S.J.2
  • 51
    • 0001568854 scopus 로고
    • Efficient implementation of essentially non-oscillatory shock capturing schemes II
    • Shu C.-W., and Osher S.J. 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.J.2
  • 52
    • 0037434586 scopus 로고    scopus 로고
    • Non-linear evolution using optimal fourth-order strong-stability-preserving Runge-Kutta methods
    • Spiteri R.J., and Ruuth S.J. Non-linear evolution using optimal fourth-order strong-stability-preserving Runge-Kutta methods. Mathematics and Computers in Simulation 62 (2003) 125-135
    • (2003) Mathematics and Computers in Simulation , vol.62 , pp. 125-135
    • Spiteri, R.J.1    Ruuth, S.J.2
  • 53
    • 0031234473 scopus 로고    scopus 로고
    • Accurate monotonicity preserving scheme with Runge-Kutta time-stepping
    • Suresh A., and Huynh H.T. Accurate monotonicity preserving scheme 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
  • 54
    • 33947386249 scopus 로고    scopus 로고
    • Arbitrary high order discontinuous Galerkin schemes fort the magnetohydrodynamic equations
    • Taube A., Dumbser M., Balsara D.S., and Munz C.D. Arbitrary high order discontinuous Galerkin schemes fort 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.S.3    Munz, C.D.4
  • 55
    • 0008392886 scopus 로고    scopus 로고
    • ADER: arbitrary high order Godunov approach
    • Titarev V.A., and Toro E.F. ADER: arbitrary high order Godunov approach. Journal of Scientific Computing 17 1-4 (2002) 609-618
    • (2002) Journal of Scientific Computing , vol.17 , Issue.1-4 , pp. 609-618
    • Titarev, V.A.1    Toro, E.F.2
  • 56
    • 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
  • 57
    • 29144466580 scopus 로고    scopus 로고
    • Derivative Riemann solvers for systems of conservation laws and ADER methods
    • Toro E.F., and Titarev V.A. Derivative Riemann solvers for systems of conservation laws and ADER methods. Journal of Computational Physics 212 1 (2006) 150-165
    • (2006) Journal of Computational Physics , vol.212 , Issue.1 , pp. 150-165
    • Toro, E.F.1    Titarev, V.A.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
  • 59
    • 84894021661 scopus 로고
    • Numerical solution of initial boundary value problems involving maxwell equation in an isotropic media
    • Yee K.S. Numerical solution of initial boundary value problems involving maxwell equation in an isotropic media. IEEE Transactions on Antenna Propagation 14 (1966) 302
    • (1966) IEEE Transactions on Antenna Propagation , vol.14 , pp. 302
    • Yee, K.S.1
  • 60
    • 0038070190 scopus 로고    scopus 로고
    • High order WENO schemes for Hamilton-Jacobi equations on triangular meshes
    • Zhang Y.-T., and Shu C.-W. High order WENO schemes for Hamilton-Jacobi equations on triangular meshes. SIAM Journal on Scientific Computing 24 (2003) 1005-1030
    • (2003) SIAM Journal on Scientific Computing , vol.24 , pp. 1005-1030
    • Zhang, Y.-T.1    Shu, C.-W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.