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

Publication at Faculty of Mathematics and Physics |
2019

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.