Numerically Efficient Solution Techniques for Computational Fluid Dynamics and Heat Transfer Problems

Abstract

We present a numerical software interface that can be integrated easily in a CFD or Heat transfer code and allows the systematic investigation of the efficiency of a broad class of solvers to optimize the code. We consider three classes of solvers that are respectively direct solver with LU decomposition, Krylov method with incomplete LU preconditionner and algebraic multigrid that have been implemented in Lapack, Sparskit, and Hypre. We systematically investigate the performance of these solvers with four test cases in ground flow, multiphase flow, bioheat transfer, and pressure solve in an Incompressible Navier Stokes code for flow in pipe with overset composite meshes. We show for each test case that the choice of the best solver may depend critically on the grid size, the aspect ratio of the grid, and further the physical parameters of the problem and the architecture of the processor. We have constructed an interface that allows to easily include in an existing CFD or heat transfer code any of the elliptic solvers available in Lapack, Sparskit and Hypre. This interface has the simplicity of Matlab command but keeps the efficiency of the original Fortran or C library. This interface can help us to investigate what would be the best solver as a preprocessing procedure. This work is a first step to construct intelligent software that will optimize an existing code automatically using the best algorithm for the application.