Tazhimbetov, Nurbek Akhmetuly2016-06-202016-06-202015-04Tazhimbetov 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/123456789/1636http://nur.nu.edu.kz/handle/123456789/1636In 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.enAttribution-NonCommercial-ShareAlike 3.0 United StatesResearch Subject CategoriesCapstone ProjectStokes flowCapstone Project