Some remarks on the flux-free finite element method for immiscible two-fluid flows

Authors:
Katsushi Ohmori;Norikazu Saito
Affiliations:
Faculty of Human Development, University of Toyama, 3190 Gofuku, Toyama 930-8555, Japan;Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8914, Japan
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 10
Cited 0

A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure. I: The concept and the preliminary numerical tests

Computer Methods in Applied Mechanics and Engineering
A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure. II: Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders

Computer Methods in Applied Mechanics and Engineering
A level set formulation of Eulerian interface capturing methods for incompressible fluid flows

Journal of Computational Physics
Level set methods: an overview and some recent results

Journal of Computational Physics
Numerical Treatment of Defective Boundary Conditions for the Navier--Stokes Equations

SIAM Journal on Numerical Analysis
Simulations of MHD flows with moving interfaces

Journal of Computational Physics
A conservative level set method for two phase flow

Journal of Computational Physics
Analysis of a Stokes interface problem

Numerische Mathematik
On the convergence of finite element solutions to the interface problem for the Stokes system

Journal of Computational and Applied Mathematics
Flux-free Finite Element Method with Lagrange Multipliers for Two-fluid Flows

Journal of Scientific Computing

Quantified Score

Hi-index	7.29

Visualization

Abstract

We give some theoretical considerations on the the flux-free finite element method for the generalized Stokes interface problem arising from the immiscible two-fluid flow problems. In the flux-free finite element method, the flux constraint is posed as another Lagrange multiplier to keep the zero-flux on the interface. As a result, the mass of each fluid is expected to be preserved at every time step. We first study the effect of discontinuous coefficients (viscosity and density) on the error of the standard finite element approximations very carefully. Then, the analysis is extended to the flux-free finite element method.