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Stable discretization of magnetohydrodynamics in bounded domains

Publication ,  Journal Article
Liu, JG; Pego, RL
Published in: Communications in Mathematical Sciences
January 1, 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. © 2010 International Press.

Duke Scholars

Published In

Communications in Mathematical Sciences

DOI

ISSN

1539-6746

Publication Date

January 1, 2010

Volume

8

Issue

1

Start / End Page

235 / 251

Related Subject Headings

  • Applied Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 1502 Banking, Finance and Investment
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

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Liu, J. G., & Pego, R. L. (2010). Stable discretization of magnetohydrodynamics in bounded domains. Communications in Mathematical Sciences, 8(1), 235–251. https://doi.org/10.4310/CMS.2010.v8.n1.a12
Liu, J. G., and R. L. Pego. “Stable discretization of magnetohydrodynamics in bounded domains.” Communications in Mathematical Sciences 8, no. 1 (January 1, 2010): 235–51. https://doi.org/10.4310/CMS.2010.v8.n1.a12.
Liu JG, Pego RL. Stable discretization of magnetohydrodynamics in bounded domains. Communications in Mathematical Sciences. 2010 Jan 1;8(1):235–51.
Liu, J. G., and R. L. Pego. “Stable discretization of magnetohydrodynamics in bounded domains.” Communications in Mathematical Sciences, vol. 8, no. 1, Jan. 2010, pp. 235–51. Scopus, doi:10.4310/CMS.2010.v8.n1.a12.
Liu JG, Pego RL. Stable discretization of magnetohydrodynamics in bounded domains. Communications in Mathematical Sciences. 2010 Jan 1;8(1):235–251.

Published In

Communications in Mathematical Sciences

DOI

ISSN

1539-6746

Publication Date

January 1, 2010

Volume

8

Issue

1

Start / End Page

235 / 251

Related Subject Headings

  • Applied Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 1502 Banking, Finance and Investment
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics