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A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations. (English) Zbl 0936.76051
J. Comput. Phys. 149, No. 2, 270-292 (1999); erratum ibid. 153, 671 (1999).
Summary: The authors present a staggered mesh strategy which directly uses the properly upwinded fluxes that are provided by a Godunov scheme. The process of directly using the upwinded fluxes relies on a duality that exists between the fluxes obtained from a higher order Godunov scheme and the electric fields in a plasma. By exploiting this duality, they are able to construct a higher order Godunov scheme that ensures that the magnetic field remains divergence-free up to the computer’s round-off error. Discuss several test problems to show that the scheme works robustly and accurately in all situations.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
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