ON A RIEMANN SOLVER FOR THREE-DIMENSIONAL RANS

The exact analytical expression for a system of both eigenvalues and right/left eigenvectors of a Jacobian matrix for the inviscid part of a two-equations differential closure 3D RANS operator split along a curvilinear coordinate is derived. Two CFD problems are considered, namely, supersonic flow over a flat plate and supersonic flow over a compression corner with separation. It is shown that application of the exact system of eigenvalues and eigenvectors to realization of the Roe approach for approximate solution of Riemann problem results in increase in convergence rate, better stability, and higher accuracy of a steady-state solution in comparison with those in the case of an approximate system.