Hyperbolic divergence cleaning for the MHD equations

Journal of Computational Physics

Volumn 175, Issue 2, 2002, Pages 645-673

  Dedner, A ^a   Kemm, F ^b   Kroner D ^a   Munz, C D ^b   Schnitzer, T ^a   Wesenberg, M ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

^b UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Divergence cleaning; Finite volume schemes; MHD equations

Indexed keywords

MAGNETOHYDRODYNAMICS;

DIVERGENCE CLEANING; DIVERGENCE CONSTRAINT; DIVERGENCE ERROR; FINITE VOLUME SCHEMES; HYPERBOLIC DIVERGENCE CLEANINGS; MAGNETOHYDRODYNAMIC EQUATIONS; MAGNETOHYDRODYNAMIC PROCESS; NEW APPROACHES; NUMERICAL SCHEME; STABILITY PROBLEM;

LAGRANGE MULTIPLIERS;

EID: 0037137996     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2001.6961     Document Type: Article

References (48)

1. Computational Investigations of Ideal Magnetohydrodynamic Plasmas with Discontinuities
2. Developing numerical fluxes with new sonic fix for MHD equations
3. On a finite-element method for solving the three-dimensional Maxwell equations
4. Linearized formulation of the Riemann problem for adiabatic and isothermal magnetohydrodynamics
5. Total variation diminishing scheme for adiabatic and isothermal magnetohydrodynamics
6. A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations
7. Shock-capturing approach and nonevolutionary solutions in magnetohydrodynamics
8. Numerical methods for gasdynamic systems on unstructured meshes
9. An entropic solver for ideal Lagrangian magnetohydrodynamics
10. Relativistic plasma simulation - Optimization of a hybrid code
11. Fluid modeling of magnetized plasmas
12. Note: The effect of nonzero ∇ · B on the numerical solution of the magnetohydrodynamic equations
13. A simulation study of east-west IMF effects on the magnetosphere
14. An upwind differencing scheme for the equations of ideal magnetohydrodynamics
15. Roe matrices for ideal MHD and systematic construction of Roe matrices for systems of conservation laws
16. An approximate Riemann solver for ideal magnetohydrodynamics
17. A simple Riemann solver and high-order Godunov schemes for hyperbolic systems of conservations laws
18. A simple finite difference scheme for multidimensional magnetohydrodynamical equations
19. A MHD-simulation in solar physics
20. Polynomial upwind schemes for hyperbolic systems
21. Flux-corrected transport techniques for multidimensional compressible magnetohydrodynamics
22. Simulation of magnetohydrodynamic flows - A constrained transport method
23. Partial Differential Equations
24. The magnetohydrodynamic Kelvin-Helmholtz instability: A two-dimensional numerical study
25. The symmetric form of magnetohydrodynamics equation
26. Finite-difference solution of Maxwell's equations in generalized nonorthogonal coordinates
27. The Least-squares Finite Element Method: Theory and Applications in Computational Fluid Dynamics and Electromagnetics
28. The origin of spurious solutions in computational electromagnetics
29. High-order upwind schemes for multidimensional magnetohydrodynamics
30. A three-dimensional modified finite volume technique for Maxwell's equations
31. On the nonlinear evolution of magnetohydrodynamic Kelvin-Helmholtz instabilities
32. A method for incorporating Gauss' law into electromagnetic PIC codes
33. Divergence corrections in the numerical simulation of electromagnetic wave propagation
34. Divergence correction techniques for Maxwell solvers based on a hyperbolic model
35. Maxwell's equations when the charge conservation is not satisfied
36. An Approximate Riemann Solver for Magnetohydrodynamics
37. A solution-adaptive upwind scheme for ideal magnetohydrodynamics
38. An upwind scheme for magnetohydrodynamics
39. A divergence-free upwind code for multidimensional magnetohydrodynamic flows
40. Multilevel preconditioning for the time-harmonic Maxwell equations
41. ZEUS2D: A radiation magnetohydrodynamics code for astrophysical flows in two space dimensions. II The magnetohydrodynamic algorithms and tests
42. Re-inventing electromagnetics: Supercomputing solution of Maxwell's equations via direct time integration on space grids
43. The ∇ · B = 0 constraint in shock-capturing magnetohydrodynamics codes
44. Comparison of some flux corrected transport and total variation diminishing numerical schemes for hydrodynamic and magnetohydrodynamic problems
45. A note on MHD Riemann solvers
46. Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media
47. Note: A higher-order Godunov method for the equations of ideal magnetohydrodynamics
48. A higher-order Godunov method for multidimensional ideal magnetohydrodynamics