Abstract
An approach to the solution of the two-dimensional Navier-Stokes equations on triangular unstructured grids is considered. The method is based on the key idea of the Godunov scheme, namely, the advisability of solving the Riemann problem of arbitrary discontinuity breakdown. In the calculations the derivatives with respect to space are approximated with both the first and the second order. However, as distinct from the conventional Godunov method, in calculating the fluxes across the cell boundaries the Riemann problem is solved using the Advection Upstream Splitting Method (AUSM). The concepts involved in the AUSM scheme are discussed. The solution of the discontinuity breakdown problem obtained within the framework of this approach is compared with the results obtained using the Godunov method. Numerical solutions of some problems of viscous and inviscid perfect-gas flows obtained on unstructured grids of different fineness and those obtained on structured grids are also compared. The effect of the spatial approximation order on the accuracy of numerical solutions is studied.
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