关键词: 三维对流扩散方程, 稀疏矩阵存储, 预条件技术, Krylov子空间方法

Abstract: The three-dimensional convection diffusion equation is discretized by the fourth order compact difference scheme, and the resulting linear algebraic system is given in the block triangular sparse matrix form. The linear algebraic system is solved by using three kinds of iterative accelerators, such as FGMRES, BICGSTAB and TFQMR, and combining with the preconditioners of incomplete factorization LU decomposition with dual threshold [(ILUT(τ,s))]. The accuracy, CPU time and iteration number under three different accelerators are compared. Moreover, the comparison of efficiency is also carried out between the traditional method with the preconditioned iterative method. Numerical results show that the preconditioned iterative method can not only ensure the accuracy of the fourth-order scheme, but also greatly improves the convergence efficiency.

Key words: three-dimensional convection-diffusion equation, sparse matrix storage, preconditioning technique, Krylov subspace methods