Local Preconditioning of the Equations of Magnetohydrodynamics and Its Numerical Applications

Abstract

An algorithm for constructing the optimal local preconditioning matrix for 2-D hyperbolic systems was developed, applied to the equations of magnetogydrodynamics (MHD), and numerically tested. In addition, local preconditioners for the 1-D Navier-Stokes (N-S) equations were reviewed and the optimal N-S preconditioner was derived. (Local preconditioning reduces the local stiffness of equation systems caused by the range of time-scales of the physical processes described.) Numerical tests of the MHD preconditioner for MHD channel flow confirmed the convergence- acceleration effect and also the additional benefit of preserving solution accuracy for low-speed flow. For low-speed flow a simplified approximate preconditioner was formulated and tested. The optimal N-S preconditioner, as expected, renders the preconditioned equations unstable for certain unlikely combinations of low Mach and Reynolds numbers.

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Document Details

Document Type
Technical Report
Publication Date
Sep 11, 2003
Accession Number
ADA417746

Entities

People

  • Bram van Leer

Organizations

  • University of Michigan

Tags

Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Channel Flow
  • Computational Fluid Dynamics
  • Computational Science
  • Convergence
  • Equations
  • Euler Equations
  • Flow
  • Fluid Dynamics
  • Magnetohydrodynamics
  • Mathematics
  • Mechanical Properties
  • Navier Stokes Equations
  • Reynolds Number
  • Two Dimensional

Readers

  • Computational Fluid Dynamics (CFD)
  • Fluid Dynamics.
  • Linear Algebra