AN IMPROVED UPWIND FINITE VOLUME RELAXATION METHOD FOR HIGH-SPEED VISCOUS FLOWS

An improved upwind relaxation algorithm for the Navier-Stokes equations is presented, and results are given from the application of the method to two test problems, including (1) a shock/boundary layer interaction on a flat plate (M∞ = 2.0) and (2) a high-speed inlet (M∞ = 5.0). The technique is restricted to high-speed (i.e., supersonic/hypersonic) viscous flows. The new algorithm depends on a partitioning of the global domain into regions or sub-domains, where a relatively thin "elliptic" region is identified near each solid wall boundary, and the remainder of the flowfield is identified to be a single larger "hyperbolic" (i.e., hyperbolic/parabolic in the streamwise direction) region. A direct solution procedure by lower/upper factorization is applied to the elliptic region(s), the results of which are then coupled to a standard line Gauss-Seidel relaxation sweep across the entire domain in the primary flow direction. In the first test problem, the new algorithm reduced total run times as much as 75% when compared to the standard alternating forward/backward vertical line Gauss-Seidel (VLGS) algorithm, whereas in the second test problem, a total savings as high as 20% was achieved. Essentially all of this improvement occurred only after the initial transient in the solution was overcome. However, in the second test problem, a significant improvement in the computational performance of the standard forward/backward VLGS algorithm was noted when overcoming the initial transient simply by converting from the use of conserved variables to primitive variables in the spatial discretization and linearizatlon of all terms. © 1992.