Abstract
A variational principle for the stream function-vorticity form of the linearised two-dimensional MHD equations which incorporates the no-slip condition as a natural boundary condition has been used to solve a range of problems. Finite element discretisations leading to sparse non-symmetric linear systems have been solved by a corrected version of a standard non-symmetric frontal solver. The numerical solutions obtained for flows over an unbounded cylinder at the larger Hartmann numbers agree with recently obtained theoretical asymptotic estimates. Other calculations for bounded flows in channels with or without obstructions are also in agreement with previous results obtained by matched asymptotic expansion methods.
Published Version
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