A fractional-step-like method for the incompressible Stokes equation, suitable for parallel multiphase problems

In this work, I present a novel numerical scheme to simulate Stokes flows at zero Reynolds number with complex fluids. The procedure is analogous to a fractional-step method, and is advantageous to adapt existing codes built to perform direct numerical simulations of inertial turbulent flows to simulate flows at vanishing Reynolds numbers. Thus, the main advantage of this procedure is that it can be coupled with existing methods used to simulate different multiphase flows, such as volume of fluid and immersed boundary methods, and can also be easily coupled to solvers for different non-Newtonian fluid models. After showing that the scheme maintains the fundamental properties of linearity and reversibility that characterise Stokes flows, I show that it can reproduce the theoretical predictions of a falling sphere in creeping flow, as well as successfully simulate elastic turbulence at zero Reynolds number.