Application of local least squares finite element method (LLSFEM) in the interface capturing of two-phase flow systems. (30th September 2018) - Mostafaiyan, Mehdi; Wießner, Sven; Heinrich, Gert; Hosseini, Mahdi Salami; Domurath, Jan; Khonakdar, Hossein Ali
Highlights: The interface can be predicted by the nodal values of volume fraction (VF). The average order of the accuracy for the surface reconstruction is 1.5. Interface curvature can be estimated by the derivatives of the VF on Gaussian points. An appropriate interface thickness must be chosen for an exact curvature calculation. LLSFEM can be used for an acceptable prediction of the second phase deformation. Droplet break up in 2D and low Reynolds simple shear flow is not possible. Abstract: 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.