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Implicit symmetrized streamfunction formulations of magnetohydrodynamics
Author(s) -
Kang K. S.,
Keyes D. E.
Publication year - 2008
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1755
Subject(s) - discretization , multigrid method , finite element method , mathematics , nonlinear system , stream function , generalized minimal residual method , computer science , mathematical analysis , linear system , partial differential equation , physics , vortex , mechanics , vorticity , quantum mechanics , thermodynamics
We apply the finite element method to the classic tilt instability problem of two‐dimensional, incompressible magnetohydrodynamics, using a streamfunction approach to enforce the divergence‐free conditions on the magnetic and velocity fields. We compare two formulations of the governing equations, the standard one based on streamfunctions and a hybrid formulation with velocities and magnetic field components. We use a finite element discretization on unstructured meshes and an implicit time discretization scheme. We use the PETSc library with index sets for parallelization. To solve the nonlinear problems on each time step, we compare two nonlinear Gauss‐Seidel‐type methods and Newton's method with several time‐step sizes. We use GMRES in PETSc with multigrid preconditioning to solve the linear subproblems within the nonlinear solvers. We also study the scalability of this simulation on a cluster. Copyright © 2008 John Wiley & Sons, Ltd.