求解二维对流扩散方程的投影迭代法

Project iterative method for solving 2D convection diffusion equation

鉴于目前流行的求解大型稀疏代数方程组的投影迭代法中,为提高迭代效率,在迭代前通常需要对稀疏矩阵进行预处理,改善迭代矩阵的条件数,从而减少迭代次数,这使得发展稀疏矩阵的存储技术变得尤为关键。基于二维对流扩散方程的四阶紧致差分格式,将其转化为代数方程组,得到其三对角块形式的系数矩阵,利用稀疏矩阵存储技术和预条件迭代法进行求解,并与传统的中心差分格式所得数值解进行比较,充分说明了方法的高效性和可靠性。

The popular project iterative methods of solving large scale algebra equations usually need to preprocess sparse matrix before iteration to improve iterative efficiency, so the condition number of the iterative matrix is lowered and the number of iterations is reduced, which makes the development of storage technique become crucial. The fourth-order compact difference scheme of the 2D convection diffusion equation is turned into algebra equations in this paper. The coefficient matrix of three diagonal form is acquired and the storage technique of sparse matrix and preconditioned iterative method are availed, and the results are compared with the traditional central difference scheme to demonstrate the high efficiency and reliability of the presented method.