Mixed finite element level set method for numerical simulation of immiscible fluids

A new realization of a finite element level set method for simulation of immiscible fluid flows is introduced and validated on numerical benchmarks. The new method involves a mixed discretization of the dependent variables, discretizing the flow variables with non-conforming RannacherTurek finite elements while keeping a simple first order conforming discretization of the level set field. A three step segregated solution approach is employed, first using a discrete projection method to decouple and compute the velocity and pressure separately, after which the level set field can be computed independently. The developed method is tested and validated on a static bubble test case and on a numerical rising bubble test case for which a very accurate benchmark solution has been established. The new approach is also compared against two commercial simulation codes, Ansys Fluent and Comsol Multiphysics, which shows that the developed method is a magnitude or more accurate and at the same time significantly faster than state of the art commercial codes.