A Comparative Study of Different Preconditioned Krylov Subspace Methods for Solving the Fully Coupled Fluid Flow Equations

摘要

One major problem with simulation of fluid flow problems using fully coupled implicit schemes is the enormous size of matrix constructed from the coefficients of the produced linear algebraic equations. Fortunately, these matrices are essentially sparse which provides many possibilities to treat them more robustly than the dense matrices. To improve the treatment, one approach is to use a combination of suitable preconditioners and Krylov subspace method KSP to solve the resulting matrices. Indeed, finding a proper combination needs lots of experience and it really is case dependent. Beside the combination itself, there are many side choices which can be used in order to optimize the effectiveness of a chosen combination. In this work, different combinations are utilized to solve the matrix of coefficients resulted from a fully implicit treatment of the incompressible Navier-Stokes equations. Then, a comparative study is launched to evaluate the performance of each combination. The primitive utilized CFD method is a finite volume element method. The results show that the best performance is achieved using GMRES with incomplete lower upper preconditioner. The impact of different parameters which affect the performance of the best combination is also investigated in order to improve the achieved performance as much as possible.