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An adaptive multiresolution method for ideal magnetohydrodynamics using divergence cleaning with parabolic-hyperbolic correction. (English) Zbl 1320.76080
Summary: We present an adaptive multiresolution method for the numerical simulation of ideal magnetohydrodynamics in two space dimensions. The discretization uses a finite volume scheme based on a Cartesian mesh and an explicit compact Runge-Kutta scheme for time integration. Harten’s cell average multiresolution allows to introduce a locally refined spatial mesh while controlling the error. The incompressibility of the magnetic field is controlled by using a Generalized Lagrangian Multiplier (GLM) approach with a mixed hyperbolic-parabolic correction. Different applications to two-dimensional problems illustrate the properties of the method. For each application CPU time and memory savings are reported and numerical aspects of the method are discussed. The accuracy of the adaptive computations is assessed by comparison with reference solutions computed on a regular fine mesh.

76M12 Finite volume methods applied to problems in fluid mechanics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
76W05 Magnetohydrodynamics and electrohydrodynamics
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