The method of fundamental solutions for the Stokes flow with the subdomain technique

The collocation version of the Method Fundamental Solutions (MFS) with subdomains is introduced in present work for solution 2D Stokes flow backward-facing-step geometry, including Dirichlet and Neumann boundary conditions. motivation inability MFS to solve such problems slits cracks due discretization a single domain. stems from artificial that difficult or impossible properly geometrically set cases. found by splitting domains into subdomains. equations equilibrium conditions at points on interface between adjacent are derived equation. A matrix simultaneously solves problem all formed solved. sensitivity study results performed comparing relative root mean square error reference obtained classical mesh-based finite volume method very fine mesh. subdomain technique verified dividing domain 2, 3 5 velocity, vorticity pressure compare well three cases while approach outstandingly poor inappropriate. paper shows proposed maintains simplicity, true meshless character accuracy where topology requires use technique.