Computations of viscous and nonviscous gas flows on unstructured grids using AUSM

In this paper, we present a method for solving 2-D Navier-Stokes equations on triangular unstructured grids. The approach is based on the key idea of the Godunov scheme - the efficiency of finding solution to the problem on the decay of an arbitrary rupture (Riemann problem). Computations are carried out with the first- and second-order space approximation. However, unlike the original Godunov method, in computations of the flows at cell interfaces, the solution to the Riemann problem is sought using the AUSM (Advection Upstream Splitting Method) scheme. The concepts involved in the AUSM scheme are discussed. The solution of the problem on the decay of an arbitrary rupture found by the proposed approach is compared with the results obtained by the Godunov method. The numerical solutions of some problems on the flow of viscous and nonviscous perfect gas obtained on unstructured grids of different quality are presented and compared with the solutions of similar problems obtained on structured grids. The influence of the order of space approximation on the accuracy of numerical solutions is considered.