多参数传热反问题的RBF-MLPG方法研究

项目名称： 多参数传热反问题的RBF-MLPG方法研究

项目编号： No.51476149

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 能源与动力工程

项目作者： 吴学红

作者单位： 郑州轻工业学院

项目金额： 83万元

中文摘要： MLPG(meshless local Petrov-Galerkin)方法具有稳定性好、计算精度高、对不规则区域适应性好等优点。近年来采用该方法计算传热与流动问题及其反问题已成为研究热点，但仍存在对流项处理方法造成的计算精度低和用于反问题时计算量大等缺点。本项目研究以径向基函数（RBF）作为MLPG方法的插值函数，应用Hermite方法构建RBF-MLPG方法的第二类边界条件处理方法，研究其稳定性及精度；借鉴有限容积法或有限元方法处理对流项的思想，构建RBF-MLPG方法的对流项迎风格式，克服假扩散现象，研究格式的健壮性、稳定性与精度；构建多参数不规则区域传热反问题的RBF-MLPG计算方法，研究其稳定性、计算精度及优化方法；研究建立多参数传热反问题的降阶模型，提高计算效率。本项目的深入研究将为传热问题及反问题的计算提供一种新方法，研究结果对丰富无网格方法理论及其工程应用具有重要意义。

中文关键词： 多参数反问题；降阶模型；迎风格式；径向基函数；MLPG方法

英文摘要： MLPG(Meshless Local Petrov-Galerkin) method have good stability and high computational precise, and can be very good application at the the irregular domain. The present meshless method has been the study focus to compute heat transfer and fluid flow problem and inverse problem, but it exits some shortcomings,such as low precise for computational method of convection term and more computational time for inverse problem,etc. In present project, the radial basis function(RBF) is applied as the trail function of MLPG method, the purpose is to construct the computational method of the second boundary condition of RBF-MLPG method based on the Hermite method, the stability and accuracy of present method is investigated. Based on the computational method of convection term in the Finite volume method(FVM) or Finite element method(FEM), the upwind scheme of convection term of RBF-MLPG method is constructed to overcome the false diffusion, and the robustness, stability and accuracy of present method is studied. The RBF-MLPG method for inverse problem of irregular domain with multi-variables is constructed. the stability, accuracy and optimized method are investigated. The reduce order model (ROM) of the inverse problem with multi-variables is consturcted to improve the computational efficiency. In-depth study of this project will provide a new method for computational heat transfer problems and inverse problems, and the investigated results have important significance to further improve the theory of meshless method and its engineering application.

英文关键词： inverse problem with multi-variables;reduce order model;upwind scheme;radial basis function;MLPG method