A parallel solution-adaptive scheme for ideal magnetohydrodynamics

14th Computational Fluid Dynamics Conference

Volumn , Issue , 1999, Pages 1-16

  Grotht, C P T ^a   De Zeeuw, D L ^a   Powell, K G ^a   Gombosi, T I ^a   Stout, Q F ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; DATA STRUCTURES; DOMAIN DECOMPOSITION METHODS; FINITE VOLUME METHOD; FLUID DYNAMICS; MAGNETOPLASMA; MAGNETOSPHERE; MEMORY ARCHITECTURE; MESH GENERATION; PARALLEL PROCESSING SYSTEMS;

ADAPTIVE MESH REFINEMENT SCHEMES; APPROXIMATE RIEMANN SOLVER; COMPUTATIONAL ROBUSTNESS; FINITE VOLUME DISCRETIZATIONS; HIERARCHICAL DATA STRUCTURE; IDEAL MAGNETOHYDRODYNAMICS; MASSIVELY PARALLEL COMPUTERS; MULTI PROCESSOR ARCHITECTURE;

MAGNETOHYDRODYNAMICS;

EID: 84983134531     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (49)

1. Brackbill, J. U., and Barnes, D. C., “The Effect of Nonzero V . B on the Numerical Solution of the Magnetohydrodynamic Equations”, J. Comput. Phys., Vol. 35, pp. 426-430, 1980.
2. Godunov, S. K., “Symmetric Form of the Equations for Magnetohydrodynamics”, Report, Computer Center, Siberian Branch of USSR Academy of Sciences, 1972.
3. Godunov, S. K., “An Interesting Class of Quasilinear Systems”, Sov. Math. Dokl., Vol. 2, pp. 947-949, 1961.
4. Powell, K. G “An Approximate Riemann Solver for Magnetohydrodynamics (That Works in More than One Dimension)”, Report 9424, ICASE, July 1994.
5. Powel1, K. G., Roe, P. L., Linde, T. J., Gombosi, T. I., and De Zeeuw, D. L., “A Solution-Adaptive Upwind Scheme for Ideal Magnetohydrodynamics”, submitted to the Journal of Computational Physics, July 1998.
6. T6th, G., and OdstrEil, D., “Comparison of Some Flux Corrected Transport and Total Variation Diminishing Numerical Schemes for Hydrodynamic and Magnetohydrodynamic Problems”, J. Comput. Phys., Vol. 128, pp. 82-100, 1996.
7. Tanaka, T., “Generation Mechanisms for Magnetosphere-Ionosphere Current Systems Deduced from a Three-Dimensional MHD Simulation of the Solar Wind-Magnetosphere-Ionosphere Coupling Processes”, J. Geophys. Res., Vol. 100, No. 7, pp. 12057-12074, 1995.
8. Godunov, S. K., “Finite-Difference Method for Numerical Computations of Discontinuous Solutions of the Equations of Fluid Dynamics”, Mat. Sb., Vol. 47, pp. 271-306, 1959.
9. van Leer, B., “Towards the Ultimate Conservative Difference Scheme. I. The Quest of Monotonicity”, In Lecture Notes in Physics, volume 18, pages 163-168, New York, 1973. Springer-Verlag.
10. van Leer, B., “Towards the Ultimate Conservative Difference Scheme. II. Monotonicity and Conservation Combined in a Second Order Scheme”, J. Comput. Phys., Vol. 14, pp. 361-370, 1974.
11. van Leer, B., “Towards the Ultimate Conservative Difference Scheme. III. Upstream-Centered Finite-Difference Schemes for Ideal Compressible Flow”, J. Comput. Phys., Vol. 23, pp. 263-275,1977.
12. van Leer, B., “Towards the Ultimate Conservative Difference Scheme. IV. A New Approach to Numerical Convection”, J. Comput. Phys., Vol. 23, pp. 276-299, 1977.
13. van Leer, B., “Towards the Ultimate Conservative Difference Scheme. V. A Second-Order Sequel to Godunov’s Method”, J. Comput. Phys., Vol. 32, pp. 101-136, 1979.
14. Roe, P. L., “Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes”, J. Comput. Phys., Vol. 43, pp. 357-372, 1981.
15. van Leer, B., “Flux-Vector Splitting for the Euler Equations”, In Lecture Notes in Physics, volume 170, page 507, New York, 4. Springer-Verlag.
16. Colella, P., and Woodward, P. R., “The Piecewise Parabolic Method (PPM) for Gas-Dynamical Simulations”, J. Comput. Phys., Vol. 54, pp. 174-210, 1984.
17. Ha.rten, A., “High Resolution Schemes for Hyperbolic Conservation Laws”, J. Comput. Phys., Vol. 49, pp. 357-393, 1983.
18. Harten, A., “On a Class of High Resolution Total-Variation-Stable Finite-Difference Schemes”, SIAM J. Numer. Anal., Vol. 21, pp. 1-23, 1984.
19. Osher, S., and Chakravarthy, S. R., “High Resolution Schemes and the Entropy Condition”, SIAM J. Numer. Anal., Vol. 21, No. 5, pp. 955-984, 1984.
20. Roe, P. L., “Generalized Formulation of TVD Lax-Wendroff Schemes”, Report 8453, ICASE, January 1984.
21. Yee, H. C., “Construction of Explicit and Implicit Symmetric TVD Schemes and Their Applications”, J. Comput. Phys., Vol. 68, pp. 151-179,1987.
22. Harten, A., Enquist, B., Osher, S., and Chakravarthy, S. R., “Uniformly High Order Accurate Essentially Non-Oscillatory Schemes, III”, J. Comput. Phys., Vol. 71, pp. 231-303, 1987.
23. Brio, M., and Wu, C. C., “An Upwind Differencing Scheme for the Equations of Ideal Magnetohydrodynamics”, J. Comput. Phys., Vol. 75, pp. 400-422, 1988.
24. Zachary, A. L., and Colella, P., “A Higher-Order Godunov Method for the Equations of Ideal Magnetohydrodynamics”, J. Comput. Phys., Vol. 99, pp. 341-347,1992.
25. Roe, P. L., and Balsara, D. S., “Notes on the Eigensystem of Magnetohydrodynamics”, SIAM J. Appl. Math., Vol. 56, No. 1, pp. 57-67, 1996.
26. Dai, W., and Woodward, P. R., ‘LAn .4pproximate Riemann Solver for Ideal Magnetohydrodynamics” , J. Comput. Phys., Vol. 111, pp. 354-372, 1994.
27. Dai W., and Woodward, P. R., “Extension of the Piecewise Parabolic Method to Multidimensional Ideal Magnetohydrodynamics”, J. Comput. Phys., Vol. 115, pp. 485-514, 1994.
28. Croisille, J.-P., Khanfir, R., and Chanteur, G., “Numerical Simulation of the MHD Equations by a Kinetic-Type Method”, SIAM J. Sci. Cornput., Vol. 10, No. 1, pp. 81-92, 1995.
29. Linde, T. J., A Three-Dimensional Adaptive Multijluid MHD Model of the Heliosphere, PhD thesis, University of Michigan, May 1998.
30. Harten, A., Lax, P. D., and van Leer, B., “On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws”, SIAM Rev., Vol. 25, No. 1, pp. 35-61, 1983.
31. Einfeldt, B., Munz, C. D., Roe, P. L., and Sjogreen, B., “On Godunov-Type Methods near Low Densities”, J. Comput. Phys., Vol. 92, pp. 273-295, 1991.
32. Barth, T. J., “Recent Developments in High Order K-Exact Reconstruction on Unstructured Meshes”, Paper 93-0668, AIAA, January 1993.
33. Powell, K. G., Roe, P. L., Myong, R. S., Gombosi, T. I., and De Zeeuw, D. L., “An Upwind Scheme for Magnetohydrodynamics”, Paper 95-1704CP, AIAA, June 1995.
34. van Leer, B., Tai, C. H., and Powell, K. G., “De sign of Optimally-Smoothing Multi-Stage Schemes for the Euler Equations”, Paper 89-1933-CP, AIAA, June 1989.
35. Berger, M. J., Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations, PhD thesis, Stanford University, January 1982.
36. Berger, M. J., “Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations”, J. Comput. Phys., Vol. 53, pp. 484-512, 1984.
37. Berger, M. J., and Colella, P., “Local Adaptive Mesh Refinement for Shock Hydrodynamics”, J. Comput. Phys., Vol. 82, pp. 67-84, 1989.
38. Berger, M. J., and LeVeque, R. J., “An Adaptive Cartesian Mesh Algorithm for the Euler Equations in Arbitrary Geometries”, Paper 89-1930, .41,4A, June 1989.
39. Berger, M. J., and Saltzman, J. S., “AMR on the CM-2”, Appl. Numer. Math., Vol. 14, pp. 239-253, 1994.
40. Quirk, J. J., An Adaptive Grid Algorithm for Computational Shock Hydrodynamics, PhD thesis, Cranfield Institute of Technology, January 1991.
41. Quirk, J. J., and Hanebutte, U. R., “A Parallel Adaptive Mesh Refinement Algorithm”, Report 93 63, ICASE, August 1993.
42. De Zeeuw, D., and Powell, K. G., “An Adaptively Refined Cartesian Mesh Solver for the Euler Equations”, J. Comput. Phys., Vol. 104, pp. 56-68, 1993.
43. Powell, K. G., Roe, P. L., and Quirk, J., “Adaptive-Mesh Algorithms for Computational Fluid Dynamics”, In Hussaini, M. Y., Kumar, -4., and Salas, M. D., editors, Algorithmic Trends in Computational Fluid Dynmaics, pages 303-337. Springer-Verlag, New York, 1993.
44. Paillbre, H., Powell, K. G., and De Zeeuw, D. L., “A Wave-Model-Based Refinement Criterion for Adaptive-Grid Computation of Compressible Flows”, Paper 93-0322, AIAA, January 1993.
45. Goodman, M. L., “A Three-Dimensional, Iterative, Mapping Procedure for the Implemenation of an Ionosphere-Magnetosphere Anisotropic Ohm’s Law Boundary Condition in Global magnetohydrodynamic Simulations”, Ann. Geophys., Vol. 13, pp. 843-853,1995.
46. Amm, O., “Comment on “A Three-dimensional, Iterative, Mapping Procedure for the Implemenation of an Ionosphere-Magnetosphere Anisotropic Ohm’s Law Boundary Condition in Global Magnetohydrodynamic Simulations” by Michael L. Goodman”, Ann. Geophys., Vol. 14, pp. 773-774, 1996.
47. Schwenn, R., and Marsch, E., editors, Physics of the Inner Heliosphere, Springer-Verlag, New York, 1990.
48. McComas, D. J., Bame, S. J., Barraclough, B. L., Feldman, W. C., Funsten, H. O., Gosling, J. T., Riley, P., Skoug, R., Balogh, A., Forsyth, R., Goldstein, B. E., and Neugebauer, M., “Ulysses’ Return to the Slow Solar Wind”, Geophys. Res. Lett., Vol. 25, No. 1, pp. 14, 1998.
49. Pneuman, G. W., and Kopp, R. A., “Gas-Magnetic Field Interactions in the Solar Corona”, Sol. Phys., Vol. 18, pp. 258-270, 1971.