A modified higher order Godunovs scheme for stiff source conservative hydrodynamics
We present an efficient second-order accurate scheme to treat stiff source terms within the framework of higher order Godunovs methods. We employ Duhamels formula to devise a modified predictor step which accounts for the effects of stiff source terms on the conservative fluxes and recovers the correct isothermal behavior in the limit of an infinite cooling/reaction rate. Source term effects on the conservative quantities are fully accounted for by means of a one-step, second-order accurate semi-implicit corrector scheme based on the deferred correction method of Dutt et al. We demonstrate the accurate, stable and convergent results of the proposed method through a set of benchmark problems for a variety of stiffness conditions and source types.
hydrodynamics godunov methods numerical methods stiff equations