A Stabilized Finite Element Formulation for Two-Phase Flow Models Using Orthogonal Subgrid-Scales
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In this contribution, we introduce approaches to the numerical modeling of multiphase flow phenomena using stabilized finite element formulations based on the Variational Multiscale Method. In particular, we focus on a dispersed flow problem involving two fluid components. Each component is assumed to satisfy the incompressible isothermal Navier-Stokes equations locally. The mixture model is obtained by averaging over a control volume and making simplified assumptions on the moment exchange due to drag forces. The resulting system of coupled partial differential equations for velocities, volume fractions, and pressure is discretized in space using finite elements. In addition to the Galerkin formulation, stabilization terms are required to achieve control of the pressure as well as the volume fractions. To this end, we employ orthogonal subgrid-scales based on a variational multiscale concept. This approach permits a 'term-by-term' stabilization, hence giving rise to an efficient and flexible scheme that is conceptually straightforward to generalize in the presence of multiple components and more complex phase interactions. We discuss the convergence properties and computational cost of the proposed approach for different finite element interpolations and present some first numerical results for several benchmark examples.
