On resistive MHD models with adaptive moving meshes

Journal of Scientific Computing

Volumn 24, Issue 2, 2005, Pages 263-284

  Zegeling, Paul A ^a  

^a UTRECHT UNIVERSITY   (Netherlands)

Author keywords

Adaptive moving mesh method; Coordinate transformation; Equidistribution principle; Implicit explicit time integration; Magnetohydrodynamics; Monitor functions

Indexed keywords

COMPUTATIONAL METHODS; ITERATIVE METHODS; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; NUMERICAL ANALYSIS; PARTIAL DIFFERENTIAL EQUATIONS;

ADAPTIVE MOVING MESH METHOD; COORDINATE TRANSFORMATION; EQUIDISTRIBUTION PRINCIPLE; IMPLICIT-EXPLICIT TIME INTEGRATION; MONITOR FUNCTIONS;

MAGNETOHYDRODYNAMICS;

EID: 23944462472     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10915-004-4618-6     Document Type: Conference Paper

References (24)

1. Ascher, U. M., Ruuth, S. J., and Wetton, B. T. R. (1995). Implicit-explicit methods for time-dependent PDE's. SIAM J. Num. Anal. 32, 797-823.
2. Beckett, G., Mackenzie, J. A., Ramage, A., and Sloan, D. M., (2001). On the numerical solution of one-dimensional PDEs using adaptive methods based on equidistribution. J. Comp. Phys. 167, 372-392.
3. Beckett, G., Mackenzie, J. A., Ramage, A., and Sloan, D. M., (2002). Computational solution of two-dimensional unsteady PDEs using moving mesh methods. J. Comp. Phys. 182, 478-495.
4. Brackbill, J. U., (1993). An adaptive grid with directional control. J. of Comp. Phys. 108, 38-50.
5. Brackbill, J. U., and Barnes, D. C., (1980). The effect of nonzero ∇·B on the numerical solution of the magnetohydrodynamic equations. J. Comp. Phys. 35, 426-430.
6. Clément, Ph., Hagmeijer, R., and Sweers, G., (1996). On the invertibility of mappings arising in 2D grid generation problems. Num. Math. 73, 37-51.
7. Davidson, P. A., (2001). An Introduction to Magneto-Hydrodynamics, Cambridge University Press, Cambridge.
8. Huang, W. and Sun, W., (2003). Variational mesh adaptation II: error estimates and monitor functions. J. Comp. Phys. 184, 619-648.
9. Huang, W., and Russell, R. D., (1999). Moving mesh strategy based on a gradient flow equation for two-dimensional problems. SIAM J. Sci. Comp. 3, 998-1015.
10. Huang, W., Zheng, L., and Zhan, X., (2002). Adaptive moving mesh methods for simulating one-dimensional groundwater problems with sharp moving fronts. Int. J. Num. Meth. Eng. 54, 1579-1603.
11. Keppens, R., Tóth, G., Westermann, R. H. J., and Goedbloed, J. P., (1999). Growth and saturation of the Kelvin-Helmholtz instability with parallel and antiparallel magnetic fields. J. Plasma Phys. 61, 1-19.
12. Keppens, R., Nool, M., Zegeling, P. A., and Goedbloed, J. P., (2000). Dynamic grid adaptation for computational magnetohydrodynamics Proc. High Performance Computing and Networking 2000. In Bubak M. et al. (eds.), Lecture Notes in Computer Science (Springer-Verlag, Berlin Heidelberg) 1823, 61-70.
13. Knupp, P., and Steinberg, S., (1993). Fundamentals of Grid Generation, CRC-Press, Inc., Boca Raton.
14. Liu, F., Ji, S., and Liao, G., (1998). An adaptive grid method and its application to steady Euler flow calculations. SIAM J. Sci. Comp. 20, 811-825.
15. Moffat, H. K., (1978). Magnetic Field Generation in Electrically Conducting Fluids, Cambridge University Press, Cambridge.
16. Tang, H. Z., and Tang, T., (2003). Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws. SIAM J. Num. Anal. 41, 487-515.
17. Trompert, R. A., (1995). Local uniform grid refinement fot time-dependent partial differential equations, CWI-tract No. 107, Centrum voor Wiskunde en Informatica, Amsterdam, 1995.
18. van der Vorst, H. A., (1992). Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Stat. Comp. 13, 631-644.
19. Weiss, N. O., (1966). The expulsion of magnetic flux by eddies, Proc. Roy. Soc. A 293, 310-328.
20. Winslow, A. M., (1981). Adaptive mesh zoning by the equipotential method, Technical Report UCID 19062.
21. Zegeling, P. A., (2004). Tensor-product adaptive grids based on coordinate transformations. J. Comp. Appl. Maths. 166, 343-360.
22. Zegeling, P. A., and Keppens, R., (2001). Adaptive MOL for magneto-hydrodynamic PDE models. In Alain Vande Wouwer, Philippe Saucez, William E. Schiesser (eds.), Adaptive Method of Lines, Chapman & Hall/CRC Press, Boca Raton pp. 117-137.
23. Zegeling, P. A., and Kok, H. P., (2004). Adaptive moving mesh computations for reaction-diffusion systems. J. Comp. Appl. Maths. 168, 519-528.
24. Ziegler, U., (1999). A three-dimensional Cartesian adaptive grid code for compressible magnetohydrodynamics. Comp. Phys. Comm. 116, 65-77.