SCAIM Seminar: Christopher Batty (UBC)

The equations of Stokes flow model fluids in scenarios where the influence of advection is essentially negligible. This is a reasonable approximation in many physical situations, and such solvers can often be used as a sub-component when tackling the full Navier-Stokes equations. Staggered grid (MAC) finite difference techniques for the Stokes problem are well-established; however, the incorporation of consistent free surface and solid boundary conditions becomes quite challenging in the presence of irregularly-shaped physical boundaries that do not align with the underlying Cartesian grid. I will present our recent work on embedded boundary methods which overcome this problem by exploiting the natural boundary conditions of a variational formulation of the Stokes PDE. The method converges at first order in velocity for a range of test cases, and leads to a symmetric positive-definite linear system to be solved, rather than the typical symmetric indefinite one. In addition to convergence plots, I will demonstrate the method's application to the coiling phenomenon exhibited by high viscosity liquids like honey and syrup, in both two and three dimensions.