Application of point- and line-implicit preconditioning in unsteady flow computations

Abstract

The emphasis of this thesis is to improve the efficiency of unsteady computation of high Reynolds number turbulent flows described by the unsteady Reynolds averaged Navier-Stokes equations with closure of Spalart-Allmaras turbulence model equation on unstructured grid. The approach is based on enhancing the nonlinear agglomeration multigrid algorithm used for solving the nonlinear system of equations arising from implicit multistep and multistage time discretizations. The kernel of the approach is to introduce a point- and line-block Jacobi implicitly preconditioning technique to the existing explicit Runge-Kutta pseudo-time smoother, in order to alleviate the discrete stiffness associated with highly stretched grids in boundary layers and consequently to improve the convergence. And the lines are identified in advance for a given computational grid along the strongest coupling direction. The preconditioners are derived grom a singly diagonally implicit Runge-Kutta method, and constructed on the basis of a first order spatial discretization, in which the first order Roe scheme and thin shear layer approximation are respectively used for convective and diffusive flux. The contribution to the preconditioners from the source terms including those of turbulence model equation is also computed term by term. To demonstrate the effectiveness, tests concerning several two- and three-demensional unsteady flows are carried out. Test results show that the overall efficiency in terms of CPU-time is improved remarkably, even for a complex wing-body-horizontal tail-vertical tail DLR-F12 configuration.