基于MQ-RBF-FD求解对流扩散方程的二阶算法

doi:10.3976/j.issn.1002-4026.2020.05.014

山东科学 ›› 2020, Vol. 33 ›› Issue (5): 113-118.doi: 10.3976/j.issn.1002-4026.2020.05.014

基于MQ-RBF-FD求解对流扩散方程的二阶算法

姚林，唐泉*

新疆师范大学数学科学学院，新疆乌鲁木齐 830017

收稿日期:2020-02-07 出版日期:2020-10-08 发布日期:2020-09-27
通信作者: 唐泉（1991—），男，硕士，研究方向为偏微分方程及其应用。E-mail:1049024093@qq.com E-mail:yaolin.wushi@foxmail.com
作者简介:姚林（1990—），男，硕士，研究方向为偏微分方程数值解。E-mail:yaolin.wushi@foxmail.com
基金资助:
新疆师范大学优秀青年教师科研启动基金（3010010100）；新疆师范大学“十三五”校级重点学科数学(20SDKD1101)

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

YAO Lin，TANG Quan *

School of Mathematical Sciences，Xinjiang Normal University, Urumqi 830017，China

Received:2020-02-07 Online:2020-10-08 Published:2020-09-27

摘要/Abstract

摘要：

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。

关键词: 对流扩散, 局部的径向基函数方法, 形状参数, 高阶精度, 迭代格式

Abstract: 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.

Key words: convection diffusion, RBF-FD method, shape parameter, higher order accuracy, iterative schemes

中图分类号:

O241.82

姚林, 唐泉. 基于MQ-RBF-FD求解对流扩散方程的二阶算法 [J]. 山东科学, 2020, 33(5): 113-118.

YAO Lin, TANG Quan. A novel second-order algorithm based on MQ-RBF-FD method for solving convection diffusion equation[J]. Shandong Science, 2020, 33(5): 113-118.

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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

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