An unstructured finite element model for incompressible two-phase flow based on a monolithic conservative level set method

We present a robust numerical method for solving incompressible, immiscible two-phase flows. The method extends both a monolithic phase conservative level set method with embedded redistancing and a semi-implicit high-order projection scheme for variable-density flows. The level set method can be initialized conveniently via a simple phase indicator field instead of a signed distance function (SDF). To process the indicator field into a SDF, we propose a new partial differential equation-based redistancing method. We also improve the monolithic level set scheme to provide more accuracy and robustness in full two-phase flow simulations. Specifically, we perform an extra step to ensure convergence to the signed distance level set function and simplify other aspects of the original scheme. Lastly, we introduce consistent artificial viscosity to stabilize the momentum equations in the context of the projection scheme. This stabilization is algebraic, has no tunable parameters and is suitable for unstructured meshes and arbitrary refinement levels. The overall methodology includes few numerical tuning parameters; however, for the wide range of problems that we solve, we identify only one parameter that strongly affects performance of the computational model and provide a value that provides accurate results across all the benchmarks presented. This methodology results in a robust, accurate, and efficient two-phase flow model, which is mass- and volume-conserving on unstructured meshes and has low user input requirements, making it attractive for real-world applications.