一种新的高效的有限体积法

有限体积法是一种新的流体力学数值计算方法,其对于数值求解流体力学中常常遇到的偏微分方程十分有效。这篇文章采用有限体积法离散得到数值逼近格式,由原来的九点格式变成现在的五点格式,减少了节点的使用个数,且系数矩阵的条件数比较小,能保证离散的方程组有唯一解,且有较高的精度,并用提出的数值解方法求解二维的Laplace方程。数值计算结果与精确解作比较,吻合良好,且降低了计算机计算时所需要的时间。

A New and Effective Finite Volume Method

Finite volume method is a new method for numerical calculation of hydrodynamics,and it is very effective for partial differential equations often encountered in numerical fluid dynamics.This article uses finite volume method to discrete numerical approximation to,changes the original nine-point format into the present five-point format,and reduces the number of node.And the condition number of coefficient matrix is smaller,so it can ensure the unique solution of the discrete equation and a higher degree of accuracy.The proposed method is used to solve the two dimensional Laplace equation.With the comparison between numerical results and exact solutions,they match well,and reduce the time needed in computer calculations.