Open Access
March 2010 Stable discretization of magnetohydrodynamics in bounded domains
Jian-Guo Liu, Robert Pego
Commun. Math. Sci. 8(1): 235-251 (March 2010).


We study a semi-implicit time-difference scheme for magnetohydrodynamics of a viscous and resistive incompressible fluid in a bounded smooth domain with a perfectly conducting boundary. In the scheme, the velocity and magnetic fields are updated by solving simple Helmholtz equations. Pressure is treated explicitly in time, by solving Poisson equations corresponding to a recently de- veloped formula for the Navier-Stokes pressure involving the commutator of Laplacian and Leray projection operators. We prove stability of the time-difference scheme, and deduce a local-time well- posedness theorem for MHD dynamics extended to ignore the divergence-free constraint on velocity and magnetic fields. These fields are divergence-free for all later time if they are initially so.


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Jian-Guo Liu. Robert Pego. "Stable discretization of magnetohydrodynamics in bounded domains." Commun. Math. Sci. 8 (1) 235 - 251, March 2010.


Published: March 2010
First available in Project Euclid: 23 February 2010

zbMATH: 1278.76127
MathSciNet: MR2655908

Primary: 76D03 , 76W05

Keywords: Leray projection , pressure Poisson equation , projection method , Stokes pressure , Time-dependent incompressible viscous flow

Rights: Copyright © 2010 International Press of Boston

Vol.8 • No. 1 • March 2010
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