Surface tension effects between two immiscible Stokes fluids: a computational study using unfitted hybrid high-order methods and a level-set scheme

We develop an unfitted Hybrid High-Order (HHO) method coupled with a level-set scheme to solve numerically the flow of two immiscible Stokes fluids separated by an unknown interface where surface tension effects are present. The interface can cut through the mesh cells and a cell-agglomeration procedure is used to prevent possible ill-conditioning caused by small cut cells. The first computational study concerns the equilibrium between pure shear flow at infinity and surface tension, leading to an interface with elliptic shape. In particular, the dependence of the capillarity number on the Taylor deformation parameter and the viscosity ratio of both fluids is investigated. The second computational study covers evolving interfaces and illustrates how an initial interface progressively relaxes toward equilibrium.