Math @ Duke

Publications [#304584] of JianGuo Liu
Papers Published
 Liu, JG; Pego, RL, Stable discretization of magnetohydrodynamics in bounded domains,
Communications in Mathematical Sciences, vol. 8 no. 1
(2010),
pp. 235251, ISSN 15396746
(last updated on 2018/10/18)
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. © 2010 International Press.


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

