Dissipation-adjustable BVD Scheme for Solving Magnetohydrodynamics Equations

Based on the boundary variation diminishing (BVD) method with adjustable numerical dissipation, a finite volume scheme for the ideal MHD equations is proposed. The proposed scheme uses the quadratic polynomial and the hyperbolic tangent function to build a hybrid spatial reconstruction and introduces a dissipation adjustment strategy in smooth regions. The scheme not only captures shock waves with high fidelity but also accurately resolves the multi-scale flow fields in smooth regions. Numerical results of typical ideal MHD test cases show that the scheme can accurately simulate complex MHD flows, with the computational accuracy and shock-capturing capability superior to traditional TVD and third-order WENO methods.