Method of regularized sources for Stokes flow problems with improved calculation of velocity derivatives at the boundary

7th European Thermal-Sciences Conference

Boidar, Šarler^1,2,3 ; Wen, Shiting^1 ; Li, Ming^1

Institute of Metals and Technology, Lepi pot 11, Ljubljana

SI-1000, Slovenia^1

University of Nova Gorica, Vipavska 13, Nova Gorica

SI-5000, Slovenia^2

College of Mathematics, Taiyuan University of Technology, Yingze West Street 79, Shanxi Province, Taiyuan

30024, China^3

关键词: Artificial boundaries;    Dirac delta function;    Dirichlet and Neumann boundary conditions;    Fundamental solutions;    Linear combinations;    Method of fundamental solutions;    Two-dimensional flow;    Velocity derivatives;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/745/3/032025/pdf
DOI  :  10.1088/1742-6596/745/3/032025

来源: IOP

【 摘 要 】

The solution of Stokes flow problems with Dirichlet and Neumann boundary conditions is performed by a non-singular Method of Fundamental Solutions which does not require artificial boundary, i.e. source points of fundamental solution coincide with the collocation points on the boundary. Instead of Dirac delta force, an exponential function, called blob, with a free parameter epsilon is employed, which limits to Dirac delta function when epsilon limits to zero. The solution of the problem is sought as a linear combination of the fields due to the regularized sources that coincide with the boundary and with their intensities chosen in such a way that the solution complies with the boundary conditions. A two-dimensional flow between parallel plates is chosen to assess the properties of the method. The results of the method are accurate except for the derivatives at the boundary. A correction of the method is proposed which can be used to properly assess also the derivatives at the boundary.