基于MQ-RBF-FD求解对流扩散方程的二阶算法

A novel second-order algorithm based on MQ-RBF-FD method for solving convection diffusion equation

提出一种新颖的二阶算法求解对流扩散方程,空间离散使用多二次元局部的径向基函数(MQ-RBF-FD)方法结合维数分裂方法,时间离散采用交替迭代格式结合二阶向后微分(BDF2)方法。找到合适的迭代数目,选择最优的形状参数c,最终获得高阶精度。提供了2个数值例子,验证了二阶算法的合理性和可行性。

To solve the unsteady convection diffusion equation,we propose a new second-order algorithm that applies the multi-quadrics localized radial basis function(MQ-RBF-FD)method and dimension-splitting method for spatial discretization,and BDF2 methods and alternating iterative schemes for temporal discretization.We determine the appropriate number of iterations,choose an optimal shape parameter c,and finally,obtain higher order accuracy.We conducted numerical experiments to verify the rationality and feasibility of the theoretical results.