Moving mesh methods for two-phase flow systems: Assessment, comparison and analysis

We seek to assess the key aspects of two modern moving mesh approaches for simulating two-phase flows where a thin explicit interface separates the two fluids within the context of "one-fluid" formula-tion. Both methods discretize the fluid equations through the Finite Element (FE) method using the Arbi-trary Lagrangian-Eulerian (ALE) framework, therefore a complex moving mesh scheme is achieved. These methods are supported by a spatial Heaviside function which locates the interface between fluids in the domain of interest. Despite a sharp geometrical definition of the tracked interface, one methodology re-quires a smooth regularization of the Heaviside function to avoid undesirable numerical instabilities. On the other hand, the second method bypass such an artificial requirement but an advanced remeshing al-gorithm is demaded to maintain the simulation. Several important test cases are used as benchmark to assess the capabilities of both approaches such as the oscillating drop and the Zalesak's disk test where fundamental parameters are evaluated and more challenging two-phase flows such as the rising of single bubbles and microscale flows in capillaries. A comparison is then made to evaluate the important aspects of each model and an accurate analysis is made to quantify the errors associated to important parameters in two-phase flows such as surface tension, liquid film thickness, interfacial waves, interface deformation and bubble/drop shape. (c) 2021 Elsevier Ltd. All rights reserved.