Implicit and semi-implicit schemes in the versatile advection code: Numerical tests

Astronomy and Astrophysics

Volumn 332, Issue 3, 1998, Pages 1159-1170

  Toth G ^a,d   Keppens, R ^b   Botchev, M A ^c  

^a UTRECHT UNIVERSITY   (Netherlands)

^b FOM INSTITUTE FOR PLASMA PHYSICS RIJNHUIZEN   (Netherlands)

^c UTRECHT UNIVERSITY   (Netherlands)

^d EÖTVÖS LORÁND UNIVERSITY   (Hungary)

Author keywords

Hydrodynamics; Magnetohydrodynamics; Methods: numerical; Shock waves

Indexed keywords

EID: 0001085487     PISSN: 00046361     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. Botchev M. A., Sleijpen G.L.G., van der Vorst H.A., 1997, Stability control for approximate implicit time-stepping schemes with minimal residual iterations, Department of Mathematics, Utrecht University, Preprint 1043, December
2. Brackbill J.U., Barnes D.C., 1980, J. Comput. Phys. 35, 426
3. Chakrabarti S.K., 1989, ApJ 347, 365
4. Chakrabarti S.K., Molteni D., 1993, ApJ 417, 671
5. Collela P., Woodward P.R., 1984, J. Comput. Phys. 54, 174
6. Harten A., 1983, J. Comput. Phys. 49, 357
7. Hairer E., Nørsett S.P., Wanner G., 1987, Solving Ordinary Differential Equations I. Nonstiff Problems. Springer series in Computational Mathematics, Springer-Verlag, vol. 8
8. Keppens R., Tóth G., Botchev M.A., van der Ploeg A., 1997, Implicit and Semi-Implicit Schemes in the Versatile Advection Code: algorithms. Submitted to Int. J. Num. Meth. Fluids (Paper I)
9. Paczýnski B., Wiita P.J., 1980, A&A 88, 23
10. Petschek H.E., 1964, Magnetic Field Annihilation. In: AAS/NASA Symposium on the Physics of Solar Flares. NASA Spec. Publ., SP-50, p. 425
11. Powell K.G., 1994, An approximate Riemann solver for magnetohydrodynamics (that works in more than one dimension). ICASE Report No 94-24, Langley, VA
12. Roe PL., 1981, J. Comput. Phys. 43, 357
13. Saad Y., Schultz M.H., 1986, SIAM J. Sci. Stat. Comput. 7(3), 856
14. Strang G., 1968, SIAM J. Numer. Anal. 5, 506
15. Tóth G., 1996, Astrophys. Lett. & Comm. 34, 245
16. Tóth G., 1997, Versatile Advection Code. In: Hertzberger B., Sloot P. (eds.) High Performance Computing and Networking Europe 1997. Lecture Notes in Computer Science, Springer-Verlag, vol. 1225, p. 253
17. Tóth G., Odstrčil D., 1996, J. Comput. Phys. 128, 82
18. van der Ploeg A., 1996, Reordering strategies and LU-decomposition of block tridiagonal matrices for parallel processing. Technical Report NM-R9618, Centrum voor Wiskunde en Informatica, October
19. van der Ploeg A., Keppens R., Tǒth G., 1997, Block Incomplete LU-preconditioners for Implicit Solution of Advection Dominated Problems. In: Hertzberger B., Sloot P. (eds.) High Performance Computing and Networking Europe 1997, Lecture Notes in Computer Science, Springer-Verlag, vol. 1225, p. 421
20. van der Vorst H.A., 1992, SIAM J. Sci. Statist. Comput. 13, 631
21. van Leer B., 1979 J. Comput. Phys. 32, 101
22. Yee H.C., 1989, A class of high-resolution explicit and implicit shock-capturing methods. NASA TM-101088