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Adaptive two- and three-dimensional multiresolution computations of resistive magnetohydrodynamics. (English) Zbl 1465.65083
The authors combine the finite volume method with an adaptive MR (Mesh Refinement) to solve numerically the resistive magnetohydrodynamic (MHD) equations. Fully adaptive computations of the resistive MHD equations are presented in two and three space dimensions using a finite volume discretization on locally refined dyadic grids. Divergence cleaning is used to control the incompressibility constraint of the magnetic field. For automatic grid adaptation a cell-averaged multiresolution analysis is applied which guarantees the precision of the adaptive computations, while reducing CPU time and memory requirements. Some discusions are dealt with issues of the open source code CARMEN-MHD. Several numerical tests are presented to illustrate the precision and efficiency of CARMEN-MHD.
MSC:
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
65T60 Numerical methods for wavelets
76W05 Magnetohydrodynamics and electrohydrodynamics
35Q35 PDEs in connection with fluid mechanics
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