Numerical simulation of two-phase flow of immiscible fluids by the finite element, discontinuous Galerkin and level-set methods

• ID: 2784, RIV: 10403537
• ISSN: 1019-7168, ISBN: not specified
• source: Advances in Computational Mathematics
• keywords: Two-phase flow; Immiscible fluids; Navier-Stokes equations; Transport level-set equation; Finite element method; BDF time discretization; Space-time discontinuous Galerkin method; Numerical exp
• authors: Eva Bezchlebova, Vít Dolejší, Miloslav Feistauer, Petr Svacek
• authors from KNM: Dolejší Vít, Feistauer Miloslav

Abstract

The subject of the paper is the numerical simulation of two-phase flow of immiscible fluids. Their motion is described by the incompressible Navier-Stokes equations with different constant density and viscosity for different fluids. The interface between the fluids is defined with the aid of the level-set method using a transport first-order hyperbolic equation. The Navier-Stokes system is equipped with initial and boundary conditions and transmission conditions on the interface between the two fluids. This system is discretized by the Taylor-Hood P2/P1 conforming finite elements in space and the second-order BDF method in time. The transport level-set problem is solved with the aid of the space-time discontinuous Galerkin method. Numerical experiments demonstrate that the developed method is accurate and robust.