A Roe scheme for ideal MHD equation on 2D adaptively refined triangular grids (Q1287986)

We present a second-order finite volume method for the solution of two-dimensional ideal MHD equations on adaptively refined triangular meshes. The numerical flux function is based on a multi-dimensional extension of the Roe scheme. If the mesh is composed only of triangles, our scheme is proved to be weakly consistent with the condition \(\nabla\cdot{\mathbf B}=0\). This property fails on a Cartesian grid. The efficiency of our refinement procedure is shown on two-dimensional MHD shock capturing simulations. \(\copyright\) Academic Press.