Divergence-free reconstruction of magnetic fields and WENO schemes for magnetohydrodynamics

摘要: In a pair of earlier papers the author showed importance divergence-free reconstruction in adaptive mesh refinement problems for magnetohydrodynamics (MHD) and same designing robust second order schemes MHD. Second accurate MHD have shown themselves to be very useful several areas science engineering. However, certain computational would much benefited if had third higher orders accuracy. this paper we show that vector fields can carried out with better than As result, design weighted essentially non-oscillatory (WENO) accuracy second. A multi-stage Runge-Kutta time integration is used ensure temporal matches spatial While achieved quite simply up time, going beyond most by using ADER-WENO are detailed companion paper. (ADER stands Arbitrary Derivative Riemann Problem.) Accuracy analysis it meet their smooth problems. Stringent tests also presented showing perform well on those tests.