Stable discretization of magnetohydrodynamics in bounded domains

Published

Journal Article

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. © 2010 International Press.

Full Text

Duke Authors

Cited Authors

  • Liu, JG; Pego, RL

Published Date

  • January 1, 2010

Published In

Volume / Issue

  • 8 / 1

Start / End Page

  • 235 - 251

International Standard Serial Number (ISSN)

  • 1539-6746

Digital Object Identifier (DOI)

  • 10.4310/CMS.2010.v8.n1.a12

Citation Source

  • Scopus