On Computations of third CAA workshop benchmark problems

Abstract

The high order Dispersion-Relation-Preserving (DRP) scheme is used to solve the first two category 1 problems of the third CAA Benchmark workshop. The perturbation equations about the mean flow are used as governing equations in solving two problems. Special non-homogeneous inflow and outflow boundary conditions are derived to generate incoming or outgoing disturbances. In order to create accurate results and keep a minimum number of grid points, a non-uniform grid system in which neighboring mesh sizes differ by a factor of 2 are used. In the area of grid interface, a combination of Tam & Webb DRP and Lele's cell-centered high order differencing scheme are implemented, not requiring any interpolation. Large oscillations typically produced by high order spatial schemes when the stencil extends across a discontinuity such as a shock are avoided by introducing three methods, namely shock perturbation relation method (SPRM), averaged mean flow discontinuity method (AMFDM) and limiter method (LM). The mean flow solutions are obtained analytically by using one dimensional isentropic flow as well as the shock relations.