Principles of Upwinding

Abstract

Since the Euler equations do only contain first derivatives in space and time they obviously have no terms expressing the presence of damping in time and space. So if we construct a numerical scheme for their solution we have to keep in mind the fact that a numerical error creeping somehow into the iterative solution process might grow over all bounds leading to the blow up of the scheme since it is not damped. The art of the program des gner is to find a mean to incorporate numerical damping into the discrete approximation of the Euler equations which is small enough to reproduce the original equations as faithful as possible, but large enough to keep the course of iterations in a well ordered time evolution towards the steady state. One tool for this purpose is the addition of a higher derivative of the flow variables, multiplied by a suited coefficient, to each line of the Euler equations. This is called the artificial viscosity approach, and is the topic of the preceding Chapter V.KeywordsMach NumberEuler EquationFlow VariableUpwind SchemeRiemann SolverThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.