COMPUTATION OF CONVECTION-DIFFUSION PROBLEMS DIFFERENCED WITH HIGH-ORDER UPWIND SCHEMES

Abstract

In this work, we investigate preconditioning techniques for the conjugate gradient method used in convection-diffusion problems differenced by a third-order upwind-biased scheme. To compute the preconditioning matrix, we use the incomplete lower-upper (ILU) decomposition method for matrices computed by the first-order and the third-order differencing schemes. Low-level fill-in is introduced to improve the convergence. For convection-dominant problems, we also investigate the effectiveness of the domain decomposition technique for the computation of the preconditioning matrix. In the computation of the transport of a passive scalar in the driven-cavity flow, we find that the ILU decomposition of the third-order coefficient matrix gives best performance if the fill-in level is high enough. However, in convection-dominant problems, for which a third-order scheme is most appropriate, the common ILU decomposition of the penta-diagonal coefficient matrix of a first-order scheme can achieve similar performance in combination with domain decomposition with a small overlap.