A Composite Explicit-Implicit Godunov Method for Unsteady Problems on Highly Stiff Grids

摘要

The present paper is devoted to the development of a composite explicit-implicit method for computing the unsteady Navier-Stokes equations on grids with a high ratio between maximal and minimal grid spacings, here referred to as stiff grids. The method implements a smooth switching between the explicit and implicit modes. In the explicit mode, which is realized in regions of a large grid spacing, the method is represented by a second order Godunov/MUSCL sceme. As a whole, the method satisfies the Max Norm Diminishing (MND) property in the linear case and is stable for any value of the time step in the case of non-linear equations.