Exponentially Derived Switching Schemes for Inviscid Flow

        A.B. Stephens and G.R. Shubin



    A class of "exponential schemes" used for singular perturbation problems
is taken and finite difference schemes for invisid 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.