Abstract
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.
Highlights
When solving problems of real life described by partial differential equations or systems of partial differential equations with boundary conditions, seldom this can be done analytically, and so, in order to find an approximate solution, numerical techniques, such as: the finite difference method, the finite element method, the finite volume method, the boundary element method, and others, have to be applied.Among these methods the literature highlights the boundary element method because of its advantages over the other, especially when dealing with fluid flows around obstacles, with problems with infinite domains
Our goal is to solve, by discretization, a singular boundary integral equation associated to the problem, and to obtain the numerical solution of the problem with a computer code made in Mathcad, based on this approach
We have considered in this approach the singular boundary integral equation with source distribution, for its simplicity, and because it is formulated in velocity terms, the primary variables of interest, a fact that offers many advantages
Summary
When solving problems of real life described by partial differential equations or systems of partial differential equations with boundary conditions, seldom this can be done analytically, and so, in order to find an approximate solution, numerical techniques, such as: the finite difference method, the finite element method, the finite volume method, the boundary element method, and others, have to be applied Among these methods the literature highlights the boundary element method because of its advantages over the other, especially when dealing with fluid flows around obstacles, with problems with infinite domains. The boundary element method is applied in order to find an improved numerical solution for a boundary value problem with a nonlinear boundary condition, namely the two-dimensional problem of the compressible fluid flow around obstacles.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
