New non-oscillatory central schemes on unstructured triangulations for hyperbolic systems of conservation laws

Journal of Computational Physics

Volumn 227, Issue 11, 2008, Pages 5736-5757

  Christov, Ivan ^a   Popov, Bojan ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Hyperbolic systems of conservation laws; Non oscillatory central Godunov type schemes; Unstructured meshes

Indexed keywords

HYPERBOLIC FUNCTIONS;

ARBITRARY GEOMETRY; BLACK BOXES; CENTRAL SCHEME; FULLY DISCRETE; GODUNOV-TYPE SCHEMES; HYPERBOLIC SYSTEMS OF CONSERVATION LAWS; LINEAR RECONSTRUCTION; NON-OSCILLATORY CENTRAL GODUNOV-TYPE SCHEME; UNSTRUCTURED MESHES; UNSTRUCTURED TRIANGULAR MESHES;

PHYSICAL PROPERTIES;

EID: 42649100960     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.02.007     Document Type: Article

References (47)

1. H. Nessyahu E. Tadmor Non-oscillatory central differencing for hyperbolic conservation laws J. Comput. Phys. 87 1990 408 463
2. B. van Leer Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method J. Comput. Phys. 32 1979 101 136
3. B. Popov O. Trifonov One-sided stability and convergence of the Nessyahu–Tadmor scheme Numer. Math. 104 2006 539 559
4. P. Arminjon M.-C. Viallon A. Madrane A finite volume extension of the Lax–Friedrichs and Nessyahu–Tadmor schemes for conservation laws on unstructured grids Int. J. Comput. Fluid Dyn. 9 1997 1 22
5. G.-S. Jiang E. Tadmor Nonoscillatory central schemes for multidimensional hyperbolic conservation laws SIAM J. Sci. Comput. 19 1998 1892 1917
6. G.-S. Jiang D. Levy C.-T. Lin S. Osher E. Tadmor High-resolution nonoscillatory central schemes with nonstaggered grids for hyperbolic conservation laws SIAM J. Numer. Anal. 35 1998 2147 2168
7. A. Kurganov E. Tadmor New high-resolution central schemes for nonlinear conservation laws and convection–diffusion equations J. Comput. Phys. 160 2000 241 282
8. A. Kurganov S. Noelle G. Petrova Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton–Jacobi equations SIAM J. Sci. Comput. 23 2001 707 740
9. P. Arminjon A. St-Cyr A. Madrane New two- and three-dimensional non-oscillatory central finite volume methods on staggered Cartesian grids Appl. Numer. Math. 40 2002 367 390
10. P. Arminjon A. St-Cyr Nessyahu–Tadmor-type central finite volume methods without predictor for 3D Cartesian and unstructured tetrahedral grids Appl. Numer. Math. 46 2003 135 155
11. A. Kurganov G. Petrova Central-upwind schemes on triangular grids for hyperbolic systems of conservation laws Numer. Methods Partial Differential Eq. 21 2005 536 552
12. A. Kurganov G. Petrova B. Popov Adaptive semi-discrete central-upwind schemes for nonconvex hyperbolic conservation laws SIAM J. Sci. Comput. 29 2007 2381 2401
13. I. Christov, B. Popov, A Jiang–Tadmor scheme on unstructured triangulations, Technical Report ISC-06-05-MATH, Institute for Scientific Computation, Texas A&M University, College Station, TX, 2006.
14. p SIAM J. Numer. Anal. 42 2004 714 737
15. 1-minimization Int. J. Numer. Anal. Mod. 4 2007 39 47
16. M.G. Gerritsen L.J. Durlofsky Modeling fluid flow in oil reservoirs Annu. Rev. Fluid Mech. 37 2005 211 238
17. M. Käser A. Iske Reservoir flow simulation by adaptive ADER schemes A. Iske T. Randen Mathematical Methods and Modelling in Hydrocarbon Exploration and Production Mathematics in Industry vol. 7 2005 Springer Berlin/Heidelberg 339 388
18. P. Knabner L. Angermann Numerical Methods for Elliptic and Parabolic Partial Differential Equations Texts in Applied Mathematics vol. 44 2003 Springer Berlin/Heidelberg
19. L.J. Durlofsky B. Engquist S. Osher Triangle based adaptive stencils for the solution of hyperbolic conservation laws J. Comput. Phys. 98 1992 64 73
20. P. Batten C. Lambert D.M. Causon Positively conservative high-resolution convection schemes for unstructured elements Int. J. Numer. Methods Eng. 39 1996 1821 1838
21. M.E. Hubbard Multidimensional slope limiters for MUSCL-type finite volume schemes on unstructured grids J. Comput. Phys. 155 1999 54 74
22. M. Wierse A new theoretically motivated higher order upwind scheme on unstructured grids of simplices Adv. Comput. Math. 7 1997 303 335
23. R. Abgrall On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation J. Comput. Phys. 114 1994 45 58
24. O. Friedrich Weighted essentially non-oscillatory schemes for the interpolation of mean values on unstructured grids J. Comput. Phys. 144 1998 194 212
25. C. Hu C.-W. Shu Weighted essentially non-oscillatory schemes on triangular meshes J. Comput. Phys. 150 1999 97 127
26. H.J. Schroll F. Svensson A bi-hyperbolic finite volume method on quadrilateral meshes J. Sci. Comput. 26 2006 237 260
27. R. Artebrant Third order accurate non-polynomial reconstruction on rectangular and triangular meshes J. Sci. Comput. 30 2007 193 221
28. C. Berthon Robustness of MUSCL schemes for 2D unstructured meshes J. Comput. Phys. 218 2006 495 509
29. B. Perthame Y. Qiu A variant of Van Leer’s method for multidimensional systems of conservation laws J. Comput. Phys. 112 1994 370 381
30. D. Kröner Numerical Schemes for Conservation Laws 1997 Wiley–Teubner Chichester, NY
31. T. Barth M. Ohlberger Finite volume methods: foundation and analysis E. Stein R. de Borst T.J.R. Hughes Encyclopedia of Computational Mechanics 2004 Wiley 1 57
32. A. Harten S. Osher Uniformly high-order accurate nonoscillatory schemes. I SIAM J. Numer. Anal. 24 1987 279 309
33. M. Käser A. Iske ADER schemes on adaptive triangular meshes for scalar conservation laws J. Comput. Phys. 205 2005 486 508
34. K.-A. Lie S. Noelle An improved quadrature rule for the flux-computation in staggered central difference schemes in multidimensions J. Sci. Comput. 18 2003 69 81
35. R.J. LeVeque Finite-Volume Methods for Hyperbolic Problems Cambridge Texts in Applied Mathematics vol. 31 2002 Cambridge University Press
36. M. Küther M. Ohlberger Adaptive second order central schemes on unstructured staggered grids T.Y. Hou E. Tadmor Hyperbolic Problems: Theory, Numerics, Applications 2003 Springer Berlin/Heidelberg 675 684
37. E.F. Kaasschieter Solving the Buckley–Leverett equation with gravity in a heterogeneous porous medium Comput. Geosci. 3 1999 23 48
38. J.E. Aarnes T. Gimse K.-A. Lie An introduction to the numerics of flow in porous media using Matlab G. Hasle K.-A. Lie E. Quak Geometric Modelling, Numerical Simulation, and Optimization: Applied Mathematics at SINTEF 2007 Springer Berlin/Heidelberg 261 302
39. A. Kurganov E. Tadmor Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers Numer. Methods Partial Differential Eq. 18 2002 584 608
40. R. Liska B. Wendroff Comparison of several difference schemes on 1D and 2D test problems for the euler equations SIAM J. Sci. Comput. 25 2003 995 1017
41. A.F. Emery An evaluation of several differencing methods for inviscid fluid flow problems J. Comput. Phys. 2 1968 306 331
42. P. Woodward P. Colella The numerical simulation of two-dimensional fluid flow with strong shocks J. Comput. Phys. 54 1984 115 173
43. G. Adamson M. Crick B. Gane O. Gurpinar J. Hardiman D. Ponting Simulation throughout the life of a reservoir Oilfield Rev. 8 1996 16 27
44. M.J. Berger P. Colella Local adaptive mesh refinement for shock hydrodynamics J. Comput. Phys. 82 1989 64 84
45. S. Noelle W. Rosenbaum M. Rumpf 3D adaptive central schemes: Part I. Algorithms for assembling the dual mesh Appl. Numer. Math. 56 2006 778 799
46. S. Karni A. Kurganov G. Petrova A smoothness indicator for adaptive algorithms for hyperbolic systems J. Comput. Phys. 178 2002 323 341
47. H. Tang T. Tang Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws SIAM J. Numer. Anal. 41 2003 487 515