Boundary Element Method for Stokes Flow in Incompressible Newtonian Fluids
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Date
2015-04
Authors
Tazhimbetov, Nurbek Akhmetuly
Journal Title
Journal ISSN
Volume Title
Publisher
Nazarbayev University School of Science and Technology
Abstract
In this thesis, I present different discretization techniques for boundary integral
method for Stokes flow in case of an incompressible Newtonian fluid. Boundary
integral method (BIM) is one of many techniques that are used to solve Partial
Differencial Equations (PDE) numerically. However, the basic advantage of the BIM
is that it reduces the problem from n-dimensional domain to n - 1; for example,
the two-dimensional square-box that contains viscous liquid can be solved by using
the values of an unkown function at the boundary of square. Nevertheless, the BIM
exhibits some challenges in finding the Green's function for a particular domain or
differential operator, solving the integral equations and, especially, in computing the
values of a complex domain. The latter one is quite diffcult because the flow diverges
at corners (exhibits singularity). The goal of this work is to derive general analytical solution for Stokes equation (in integral equations form) and to compute the discretized integral equations using different quadrature rules for cavity problem.
Description
Keywords
Research Subject Categories, Capstone Project, Stokes flow
Citation
Tazhimbetov Nurbek Akhmetuly. 2015. Boundary Element Method for Stokes Flow in Incompressible Newtonian Fluids. School of Science and Technology. Mathematics Department. http://nur.nu.edu.kz/handle/123456789/1636