求解Navier-Stokes方程最优控制问题的移动网格方法  

Moving Mesh Method and Its Applications in Solving Optimal Control Problems of Navier-Stokes Equation

作　　者：段献葆[1] 秦玲 党妍 DUAN Xian-bao;QIN Ling;DANG Yan(School of Sciences,Xi'an University of Technology,Xi'an 710048,China)

机构地区：[1]西安理工大学理学院,陕西西安710048

出　　处：《数学的实践与认识》2020年第17期231-238,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11971377,11601410);陕西省重点研发计划项目(2017GY-090)。

摘　　要：提出了一种受偏微分方程约束最优控制问题的移动网格方法,并以NavierStokes方程为状态方程进行了研究.所采用的网格移动策略中节点距离的移动是通过求解一个扩散方程得到.设计出了有效的求解流体力学最优控制问题的算法,给出了算法的实施过程.提供的数值算例说明所提算法可以在保证高精度数值解的前提下稳定、高效的求解最优控制问题.A moving grid method for optimal control problems constrained by partial differential equations is proposed,and the Navier-Stokes equation is used as the state equation.The moving distance of the nodes in the proposed strategy achieved by solving a diffusion equation.An effective algorithm for solving optimal control problems in fluid mechanics is provided.The implementation process of the algorithm is also given.Numerical example is provided to show that the proposed algorithm could solve the optimal control problem stably and efficiently on the premise of ensuring high precision.

关 键 词：移动网格方法 最优控制问题 有限元方法 NAVIER-STOKES方程 

分 类 号：O232[理学—运筹学与控制论]