高阶高度非线性强耦合偏微分方程组数值解实现方法——以渗蚀强耦合偏微分方程组为例  

Numerical Solution Method for High-order Highly Nonlinear Strongly Coupled Partial Differential Equations:Taking the Strongly Coupled Partial Differential Equations Describing Suffusion as an Example

作　　者：魏海江 薛瑞 梁刚 曹成 杨天 张訢炜 WEI Haijiang;XUE Rui;LIANG Gang;CAO Cheng;YANG Tian;ZHANG Xinwei(Northwest Electric Power Design Institute Co.,Ltd.of China Power Engineering Consulting Group,Xi'an 710075,China;School of Mechanical and Electronic Engineering,Jingdezhen University,Jingdezhen 333400,China;State Key Laboratory of Eco-Hydraulics in Northwest Arid Region of China,Xi'an University of Technology,Xi'an 710048,China;College of Safety Science and Engineering,Xi'an University of Science and Technology,Xi'an 710054,China)

机构地区：[1]中国电力工程顾问集团西北电力设计院有限公司,西安710075 [2]景德镇学院机械电子工程学院,江西景德镇333400 [3]西安理工大学西北旱区生态水利国家重点实验室,西安710048 [4]西安科技大学安全科学与工程学院,西安710054

出　　处：《景德镇学院学报》2024年第3期1-6,共6页Journal of JingDeZhen University

基　　金：国家自然科学基金项目(52209167);江西省教育厅科技研究项目(GJJ202807)。

摘　　要：为实现高阶高度非线性强耦合偏微分方程组(Partial Differential Equations,PDEs)的数值求解,本文以渗蚀强耦合PDEs为典型案例,剖析了PDEs的高阶高度非线性,结合空间映射,基于弱形式建模与分离式算法,实现了渗蚀强耦合PDEs的数值求解,并验证了求解方法的可行性与可靠性。研究表明:强耦合是导致PDEs非线性特性的充分条件;非弱形式建模难以妥善解决高阶高度非线性强耦合PDEs数值收敛性问题;分离式求解算法对于高阶高度非线性强耦合PDEs的初始条件更具包容性。To solve the high-order highly nonlinear strongly coupled Partial Differential Equations(PDEs),this paper takes the PDEs describing suffusion as a typical case,analyzes the high-order highly nonlinear of PDEs,combines spatial mapping,based on weak form modeling and segregated approach,realizes the numerical solution of PDEs describing suffusion,and verifies the feasibility and reliability of the solution method.The results show that strong coupling is a sufficient condition for PDEs to have nonlinearity.Without the help of weak form of PDEs,it will be difficult to solve the nonlinearity of strongly coupled models;Segregated approach is more inclusive to the initial guess of transient strongly coupled PDEs.

关 键 词：多场强耦合PDEs 高阶高度非线性 弱形式 求解方法 

分 类 号：O175.29[理学—数学]