UC Merced

Droplets and particles are a physical feature of many atmospheric and oceanic systems. For example, the Deepwater Horizon oil spill in 2010 resulted in large plumes being trapped as they rose through stratified layers in the Gulf of Mexico. To begin understanding how and why these plumes became trapped, we produce numerical simulations of a single oil droplet rising in a stratified ambient flow and develop a force decomposition model to characterize surface forces acting on the droplet. Following this, we shift towards the development of numerical methods capable of simulating incompressible flow. We develop 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 octree/quadtree grids 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 due to their simplified code structure and second order accuracy. We demonstrate its capabilities through a variety of density and surface tension driven multi-phase flows, including high fidelity simulations of single and multiple rising bubbles facing weak and strong surface deformations, as well as, flow of rising bubbles past solid obstructions.