Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows, II: Minimization of ∇·B Numerical Error

An adaptive numerical dissipation control in a class of high order filter methods for compressible MHD equations is systematically discussed. The filter schemes consist of a divergence-free preserving high order spatial base scheme with a filter approach which can be divergence-free preserving depending on the type of filter operator being used, the method of applying the filter step, and the type of flow problem to be considered. Some of these filter variants provide a natural and efficient way for the minimization of the divergence of the magnetic field (驴·B) numerical error in the sense that commonly used divergence cleaning is not required. Numerical experiments presented emphasize the performance of the 驴·B numerical error. Many levels of grid refinement and detailed comparison of the filter methods with several commonly used compressible MHD shock-capturing schemes will be illustrated