An Adaptive Mesh Refinement Solver for Multiphase Incompressible Flows with Large Density Ratios

In the present work a Navier-Stokes solver applicable to multiphase incompressible flows is presented. The solver employs level set techniques to sharply define the interface between different phases. The solver is designed to handle multiphase flows with large density ratios, such as air and water whose density ratio is 1:1,000. Adaptive mesh refinement (AMR) is used to mitigate mass loss attributed to numerical errors in level set methods where the interface is under-resolved. In the present work the mesh is selectively refined around the multiphase interface, which is evolving in time. This feature allows for sufficient resolution of complex interfacial features without over-resolving areas of no interest. A fractional step method is used to solve the momentum and continuity equations, which results in a variable coefficient Poisson pressure equation. Proper jump conditions are applied to the Poisson pressure equation to accurately capture the jump in pressure that results from surface tension between different phases. A pressure equation solution algorithm is presented that takes advantage of underlying AMR data structures. A wide range of applicable multiphase problems will be presented to demonstrate the accuracy of the solver.