A SHOCK-ADAPTIVE GODUNOV SCHEME BASED ON THE GENERALIZED LAGRANGIAN FORMULATION

Application of the Godunov scheme to the Euler equations of gas dynamics based on the Eulerian formulation of flow smears discontinuities, sliplines especially, over several computational cells, while the accuracy in the smooth flow region is of the order (h), where h is the cell width. Based on the generalised Lagrangian formulation (GLF) of Hui at al., the Godunov scheme yields superior accuracy. By the use of coordinate streamlines in the GLF, the slip-line - itself a streamline - is resolved crisply. Infinite shock resolution is achieved through the splitting of shock-cells. An improved entropy-conservation formulation of the governing equations is also proposed for computations in smooth flow regions. Finally, the use of the GLF substantially simplifies the programming logic resulting in a very robust, accurate, and efficient scheme. (C) 1995 Academic Press, Inc