Exponentially Derived Switching Schemes for Inviscid Flow
Abstract
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 oneequation 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.
 Publication:

Journal of Computational Physics
 Pub Date:
 August 1984
 DOI:
 10.1016/00219991(84)900019
 Bibcode:
 1984JCoPh..55..175S
 Keywords:

 Computational Fluid Dynamics;
 Ducted Flow;
 Inviscid Flow;
 Numerical Flow Visualization;
 One Dimensional Flow;
 Shock Waves;
 Burger Equation;
 Euler Equations Of Motion;
 Exponential Functions;
 Finite Difference Theory;
 Mach Number;
 Reynolds Number;
 Steady State;
 Viscous Flow;
 Fluid Mechanics and Heat Transfer