Computational fluid dynamics, viscous flow, Wei Shyy, Univ. Florida. Matrices: shyy161.rua, shyy41.rua From: Prof. Wei Shyy Aerospace Engineering, Mechanics & Engineering Science 231 Aerospace Building P.O. Box 116250 University of Florida Gainesville, FL 32611-6250 USA email: wss :at the domain: tiger.aero.ufl.edu phone: (904) 392-6416 Matrices are derived from a direct, fully-coupled method for solving the Navier-Stokes equations for viscous flow calculations (in which the pressure and velocity fields are coupled within the same linear system). A body-fitted co-ordinate system is used. This method is less sensitive to variations in parameters (such as the Reynolds number) than decoupled methods, in which the pressure equation is artificially derived by combining the momentum and continuity equations. Reference: Braaten, M.E. and Shyy, W., "Comparison of Iterative and Direct Solution Methods for Viscous Flow Calculations in Body-Fitted Coordinates," Inter. J. Numer. Meths. in Fluids, vol 6, pp. 325-349, 1986. NOTE: these matrices give large errors and residuals when factorized. They are linear systems from early on in the nonlinear iteration. A seemingly poor solution to these linear systems is OK, since the solution still moves the nonlinear iteration in the right direction. For example, Mups (multifrontal code) gives the following for shyy41.rua (with a right-hand-side of b(i)=n/i): maxnorm (Ax-b) 2.2e+68 maxnorm (A) 1.9e+02 maxnorm (x) 2.9e+67 maxnorm(b-Ax)/maxnorm(Ax) 3.9E-02 Minor change 3/31/03: "rua" changed to "RUA" in both files.