Exponentially Derived Switching Schemes for Inviscid Flow

A class of "exponential schemes" used for singular perturbation problems is taken and finite difference schemes for inviscid flow with shocks is derived from them. In particular, exponential schemes are formulated for steady viscous flow in a variable area duct using both a one-equation model (with the physical viscous terms) and the Euler equations (with artificial viscosity). Upon taking the limit as the viscosity coefficient goes to zero, "exponentially derived switching (EDS) schemes" are obtained which switch the direction of finite differencing based upon characteristic directions of the reduced problem. For the Euler equations some of the EDS schemes can be identified as flux vector splitting, the split coefficient matrix method, and a scheme of Huang. Some aspects of uniqueness of finite difference solutions are discussed.