A finite element technique combined with gas-liquid two-phase flow calculation for unsteady free surface flow problems

Abstract A numerical method based on the finite element method is presented for the analysis of two-dimensional viscous incompressible flows with free surfaces. The problem is formulated as a gas-liquid two-phase flow problem by adding the gaseous region adjacent to liquid region in a solution domain. A free surface is regarded as the surface of density discontinuity between gas and liquid and is not a part of boundaries of a solution domain. The present method has removed the handling of moving boundaries from numerical computations, and it has enabled us to assemble a simple algorithm for stable computations. The motion of the surface of density discontinuity is calculated by solving an advection equation derived from the equation of continuity. For that calculation, a new upwind scheme has been devised by applying the method of characteristic lines. The ability of the present method has been tested by solving three numerical examples: the broken-dam problem, the dynamic behavior of liquid drop squirted from a nozzle, and the Kelvin-Helmholtz instability. Encouraging results have been obtained.

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