LU methods for the compressible Navier-Stokes equations

Some LU methods with emphasis on the strongly implicit procedure are examined and used to obtain numerical solutions of the compressible Navier-Stokes equations in conservative form. In order to gain insight into the applicability and relative efficiency of LU methods for hyperbolic and elliptic problems, the performance of various LU methods are compared with the delta form ADI scheme for some linear model problems. In contrast to the spatially split Douglas-Gunn type methods, the strongly implicit procedure is shown to be numerically stable for the three-dimensional wave equation. The method is applied to a variety of external and internal two-dimensional flow problems involving shock wave boundary-layer interaction for both laminar and turbulent flows. The results are in good agreement with other methods and/or experiments. The storage penalty associated with the method is discussed and a simple, yet effective, means of minimizing the problem is presented.