Sharp, stable, and collocated numerical simulation of incompressible, multi-phase fluid flows

Motivated by atmospheric and oceanic applications, we present a novel collocated projection method for simulating incompressible multi-phase fluid flows in two and three dimensions. This method uses a modified pressure correction projection to solve the Navier-Stokes equations for the fluid flow. The fluid solver employs an adaptive mesh refinement strategy using non-graded quad/octrees and a finite volume discretization for the viscosity and projection operators. The moving interface between phases is captured using a coupled level set-reference map method, which provides a sharp representation of the interface position. This method and solver are highly adaptable to multi-physics applications. We demonstrate its capabilities through a variety of two and three dimensional density and surface tension driven multi-phase flows. We will present high fidelity simulations of single and multiple rising bubbles facing weak and strong surface deformations, as well as, fluid-solid coupling through rising bubbles flowing past solid obstructions. We additionally highlight the capability of this solver to study environmental applications by showing results of a rising oil droplet in a density stratified flow.