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A phase conservative, monolithic level-set method with built-in redistancing

Banff International Research Station for Mathematical Innovation and Discovery

In fluid mechanics the interaction of fluids with distinguishable material properties (e.g. water and air) is referred as multiphase flow. In this work we consider two-phase incompressible flow and concentrate on the representation and time evolution of the interface. There is an extensive list of methods to treat material interfaces. Popular choices include the volume of fluid and level set techniques. We propose a novel level-set like methodology for multiphase flow that preserves the initial mass of each phase. The model combines and reconciles ideas from the volume of fluid and level set methods by solving a non-linear conservation law for a regularized Heaviside of the (distance function) level-set. This guarantees conservation of the volume enclosed by the zero level-set. The equation is regularized by a consistent term that assures a non-singular Jacobian. In addition, the regularization term penalizes deviations from the distance function. The result is a nonlinear monolithic model for a phase conservative level-set where the level-set is given by the distance function. The continuous model is monolithic; meaning that only one equation is needed, doesnâ t require any post-processing like: numerical stabilization, re-distancing, artificial compression, flux limiting and others, all of which are commonly used in either level-set or volume of fluid methods. In addition, we have only one parameter that controls the strength of regularization/penalization in the model. We start the presentation reviewing the main ingredients of this model: 1) a conservative level-set method by [Kees et all (2011)], which combines a distanced, non-conservative level-set method with the volume of fluid method via a non-linear correction and 2) elliptic re-distancing by [Basting and Kuzmin(2014)]. Afterwards, we manipulate the conservative level-set method by [Kees et all (2011)] to motivate our formulation. We present a first model which we then modify to resolve some difficulties. Finally, we present a full discretization given by continuous Galerkin Finite Elements in space and a high-order Implicit-Explicit time integration. We demonstrate the behavior of this model by solving different benchmark problems in the literature of level-set methods. Then, we present results of this model coupled with a Navier-Stokes solver to simulate water-air interaction problems in two and three dimensions.

Mathematics; Numerical analysis; Partial differential equations

video/mp4

Author affiliation: U.S. Army Corps of Engineers

2019-03-17

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/68835

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/