An improved numerical solution of the singular boundary integral equation of the compressible fluid flow around obstacles using modified shape functions

Boundary value problems

Luminia Grecu¹ 

[1] Department of Applied Mathematics, University of Craiova, Craiova, Romania

关键词: discretization;    boundary element method;    cubic boundary element;    singular boundary integral equation;    modified shape functions;    65N38;    76M15;    76G25;    35Q35;   

DOI  :  10.1186/s13661-015-0294-8

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this work an improved numerical solution of the singular boundary integral equation of the 2D compressible fluid flow around obstacles is obtained by a boundary element method based on modified shape functions and cubic boundary elements. The singular boundary integral equation with sources distribution is considered in this paper, and for its discretization cubic boundary elements are used. The integrals of singular kernels are evaluated using modified shape functions which are deduced by using series expansions for the basis functions we choose for the local approximation models. A computer code is made using Mathcad programming language and, based on it, some particular cases are solved. In order to validate the proposed method, comparisons between numerical solutions and exact ones are performed for the considered test problems. The advantage of using modified shape functions for evaluating the singularities is pointed out through a comparison study between the numerical solution obtained by the method proposed in this paper and the one obtained by using a truncation method for evaluating the singularities.

【 授权许可】

CC BY