AN IMPLICIT EXPLICIT EULERIAN GODUNOV SCHEME FOR COMPRESSIBLE FLOW

A hybrid implicit-explicit scheme is developed for Eulerian hydrodynam ics. The hybridization is a continuous switch and operates on each cha racteristic field separately. The explicit scheme is a version of the second-order Godunov scheme; the implicit method is only first-order a ccurate in time but leads to a block tridiagonal matrix inversion for efficiency and is unconditionally stable for the case of linear advect ion. The methodology is described for the cases of linear advection, f or nonlinear scalar problems, and for gas dynamics. An important eleme nt of our work is the use of a modified Engquist-Osher flux function i n place of the Godunov flux. Several numerical results are presented t o demonstrate the properties of the method, especially stable numerica l shocks at very high CFL numbers and second-order accurate steady sta tes. (C) 1995 Academic Press, Inc.