A split-coefficient/locally monotonic scheme for multishocked supersonic flow

Abstract

A new finite-difference technique is developed for solving three-dimensional, steady, in viscid, supersonic, equilibrium real-gas flows with embedded shock waves. The technique employs the split-coefficient matrix (SCM) method to solve the gasdynamic equations in the form of decoupled compatibility relations. In the SCM technique the coefficient matrices are split according to the sign of their eigenvalues. The derivatives associated with each split-coefficient matrix are approximated by one-sided difference operators consistent with signal propagation paths. The results demonstrate that problems of conventional finite-difference methods with nonorthogonal grids are alleviated in the SCM approach. In addition, the solutions obtained using the SCM technique show that strong crossflow gradients, including crossflow shocks, can be accurately computed. To treat flows containing embedded stream wise shock waves the SCM technique is replaced, at grid points detected to be in the vicinity of a shock, by the monotonic self-adjusting hybrid/artificial compression method (ACM). The governing equations are cast in conservation law form in the shock-capturing ACM approach with damping terms added to eliminate postshock oscillations. Streamwise shocks of sufficient strength to cause conventional shock-capturing methods to fail are resolved using the combined SCM/ACM technique.