摘要
为了减少解在较小的局部区域内有着很强的奇异性、剧烈变化等的偏微分方程求解问题的计算量,提出了一种基于方程求解的移动网格方法,并将其应用于二维不可压缩Navier-Stokes方程的求解.与已有的大部分移动网格方法不同,网格节点的移动距离是通过求解一个变系数扩散方程得到的,避免了做区域映射,也不需要对控制函数进行磨光处理,所以算法很容易编程实现.数值算例表明所提算法能够在解梯度较大的位置加密网格,从而在保证提高数值解的分辨率的前提下,可以很好地节省了计算量.由于Navier-Stokes的典型性,所得算法能够推广到求解很大一类偏微分方程数值问题.
In order to reduce the computational cost of solving partial differential equation(PDE), whose solution has strong singularity or drastic change in a small local area, a moving mesh method based on equation solution is proposed and applied to solve the two-dimensional incompressible Navier-Stokes equations. Different from the most existing moving mesh methods, the moving distance of the nodes is obtained by solving a variable-coefficient diffusion equation, which avoids regional mapping and does not need to smooth the monitoring function,so the algorithm is easier to program and implement. Numerical examples show that the proposed algorithm can refine the mesh in the position where the gradient of the solution changed drastically, which can save a lot of computation time on the premise of improving the resolution of the numerical solution. Due to the typicality of the Navier-Stokes equations, the proposed algorithm can be generalized to solve many similar partial differential equations numerically.
引文
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