An unsplit Godunov method for ideal MHD via constrained transport

摘要: We describe a single step, second-order accurate Godunov scheme for ideal MHD based on combining the piecewise parabolic method (PPM) performing spatial reconstruction, corner transport upwind (CTU) of Colella multidimensional integration, and constrained (CT) algorithm preserving divergence-free constraint magnetic field. adopt most compact form CT, which requires field be represented by area-averages at cell faces. demonstrate that fluxes area-averaged used CT can made consistent with volume-averaged returned Riemann solver if they obey certain simple relationships. use these relationships to derive new algorithms constructing grid corners reduce exactly equivalent one-dimensional plane-parallel, grid-aligned flow. show PPM reconstruction must include terms MHD, we number important extensions CTU in order it CT. present results variety test problems is robust.