Three dimensional hypersonic flow simulations with the cscm implicit upwind navier-stokes method

Abstract

The computationally efficient three dimensional CSCM Navier-Stokes method of Bardina and Lombard has been extended to simulate complex external flows of hypersonic reentry vehicles at angle-of-attack. The stability and robustness of the shock capturing method has been improved with the addition of flux limiters and an inner approximation procedure in grid cells where changes of eigenvalue sign are present. The 3-D CSCM conservativesupra-characteristic method combines the best features of data management and computational efficiency of space marching procedures with the generality and stability of time dependent procedures to solve flows with mixed subsonic and supersonic zones, including streamwise separated flows. The robust stability of the method derives from the combination of conservative implicit upwind flux difference splitting, three-dimensional diagonally-dominant approximate factorization and relaxation scheme, and well-posed characteristic-based implicit boundary approximations. The efficiency of the method is based on an implicit symmetric Gauss-Seidel “method of planes” relaxation scheme with alternating directional space marching sweeps along the flow coordinate direction. A NewtonRaphson inner iteration procedure is employed with the implicit block-tridiagonal diagonally-dominant approximate factorization relaxation scheme for solution within the marching planes. This method requires less data in central memory and less total transfers of data into central memory per iteration than two data level linearized implicit schemes using only time-dependent approximate factorizations; therefore, the capability of processing larger and/or more complex data bases and computational grids is available. The efficiency of the 3-D CSCM algorithm makes this method very attractive to develop numerical procedures with equilibrium and nonequilibrium chemically reacting gases as is required for the simulation of hypersonic flows around vehicles flying at high altitudes. Here this method is applied to simulate three dimensional hypersonic flows of a perfect gas around a spherecone-cylinder-flare reentry vehicle (RV) under angle of attack. The complex flow structures around the reentry vehicle under perfect gas conditions are well captured in a few hundred iterations. Results of the numerical simulation of the flow around the reentry vehicle under free stream angles of attack of 0° and 10° are presented, together with the results of the two-dimensional code for the simulation of the axisymmetric flow. Comparison shows excellent agreement between the two codes in the axisymmetric flow case.