Turbulent flow computations on adaptive unstructured grids using a coupled discrete Newton GMRES solver

Abstract

This paper presents an implementation of the Streamline Diffusion (SD) finite element method using a coupled discrete Newton procedure to solve the continuity and momentum equations. The Jacobian is calculated using difference approximations, taking it's extreme sparsity into account and thus reducing the work required to set up the Jacobian significantly. The resulting nonsymmetric linear system is solved using the Generalized Minimal Residual (GMRES) iterative method with an Incomplete LU (ILU) preconditioner, and we address the convergence problem of GMRES when the Jacobian becomes very ill-conditioned. The turbulence model used is the standard k — e model with a near-wall modification, and the transport equations for k and 6 are solved coupled together using the method described above. The method is applied to some well known laminar and turbulent test cases, showing the high accuracy of the SD method and the convergence properties of the solver. A simple error estimate for the Navier-Stokes equations is used to refine the meshes in a relatively efficient way.