Math @ Duke

Publications [#246928] of JianGuo Liu
Papers Published
 Liu, JG; Pego, RL, STABLE DISCRETIZATION OF MAGNETOHYDRODYNAMICS IN BOUNDED DOMAINS,
Communications in Mathematical Sciences, vol. 8 no. 1
(March, 2010),
pp. 234251, INT PRESS BOSTON, INC, ISSN 15396746
(last updated on 2019/06/25)
Abstract: We study a semiimplicit timedifference 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 developed formula for the NavierStokes pressure involving the commutator of Laplacian and Leray projection operators. We prove stability of the timedifference scheme, and deduce a localtime wellposedness theorem for MHD dynamics extended to ignore the divergencefree constraint on velocity and magnetic fields. These fields are divergencefree for all later time if they are initially so. Â© 2010 International Press.


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