Nonlinear Galerkin methods based on the concept of determining modes for the magnetohydrodynamic equations. (English) Zbl 0955.76073

Summary: A new nonlinear Galerkin method based on an approximate inertial manifold and on a finite number of determining modes has been implemented for the three-dimensional magnetohydrodynamic equations. It is found that these active modes, which regulate the dynamics of the system, are not necessarily those with the smallest wavenumbers but those containing most of the time-averaged enstrophy. It is demonstrated that, owing to the reduced number of equations, the modified nonlinear Galerkin method, which includes only these determining modes in a truncation, improves the computational efficiency in comparison with the traditional Galerkin method.


76M25 Other numerical methods (fluid mechanics) (MSC2010)
76W05 Magnetohydrodynamics and electrohydrodynamics
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