Publications [#304584] of Jian-Guo Liu

Papers Published

1. Liu, JG; Pego, RL, Stable discretization of magnetohydrodynamics in bounded domains, Communications in Mathematical Sciences, vol. 8 no. 1 (January, 2010), pp. 235-251, International Press of Boston, ISSN 1539-6746
   (last updated on 2024/04/15)

   Abstract:
   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.