Application of local least squares finite element method (LLSFEM) in the interface capturing of two-phase flow systems

A least squares finite element method (LSFEM) is applied locally for the prediction of the interface advection in a two-phase flow system. Moreover, a phantom element is introduced, which determines the nodal values of the volume fractions at the onset of the flow, and provides a highly satisfactory reconstructed interface at the same time. The quality of the interface reconstruction is also examined after advection and the interface tangent, as an important parameter in the surface tension calculations, is estimated by the derivatives of the volume fraction on the Gaussian points in the vicinity of the interface intersections. The validity of the method is examined by comparing the results of the drop deformation for various Reynolds numbers with available data in the literature. Finally, some explanatory examples are provided to evaluate our suggested procedure.