Stokes Equation Solution Using the Localized Method of Fundamental Solutions With a Global Basis

Abstract

The paper focuses on deriving a local variant of the method of fundamental solutions (MFS) for the case of Stokes flow. Compared to the global and local basis variants, the local with global basis one leads to a sparse characteristic matrix as in fully localized variants but with a narrower system of equations and thus makes the solution of especially large-scale problems more efficient. It is also essential to keep the condition number of the characteristic matrix within reasonable bounds and remove the solution dependency on fictitious sources. A combination of MFS and finite collocation approach was used for the localization with a globally defined Stokeslet fundamental solution. The results of the particular local variant were compared on several examples, and the dependence of the solution on the density of the point network and the dimensions of the stencil used were also tested in the paper.