Petrov-Galerkin finite element method for gas–liquid two-phase flow based on an incompressible two-fluid model Original Research Article

An upstream finite element method for gas–liquid two-phase flow, based on an incompressible two-fluid model, is proposed in this paper. The solution algorithm is parallel to a fractional step method, and the Petrov-Galerkin method using an exponential weighting function is employed for the formulation. A quadrilateral element with four nodes is used for the discretization of the calculating domain. The present finite element method is also applied to the two-dimensional calculation of air–water two-phase flows around a rectangular cylinder in order to confirm its validity. The calculated flows exhibit unsteady behavior with the von Kármán vortices shedding from the cylinder into the wake. The volumetric fraction of the gas-phase achieves maximum value at the center of the vortices, where the pressure reaches its minimum value. These results are favorably compared with the existing calculations by a finite difference method. This suggests the present method is usefully applicable to two-phase flow analyses.