Grid Convergence Index (GCI) Analysis of the Computational Mesh Resolution for Two Numerical Simulation Schemes for the Liquid-Gas Interfacial Reconstruction/Advection in Micron and Submicron Scales*

We assessed the computational grid independence (GCI) [1] of two OpenFOAM built-in solvers to investigate the accuracy of their interfacial reconstruction and advection schemes in micron and submicron scales.  For the case of a perturbed cylindrical column collapse [2], the flow is assumed to be transient, incompressible, and immiscible. The free surface is modeled with a compressive flux in the MULES [3] solver within the interFoam [3] solver while it is modeled with geometric fluxing in the isoAdvector [4] solver which is a subroutine of the interIsoFoam [5] solver. The two solvers, namely interFoam and interIsoFoam, allow for the simulation of the two-phase Navier Stokes equations with a free surface. Adaptive Mesh Refinement (AMR) near the interface is used to better resolve the flow regions in the vicinity of the liquid-gas interface. Since the surface tension is primarily responsible for generating an increased pressure inside the liquid, GCI analysis [1] was done on the average relative pressure over the simulation domain. For the test cases with the cylindrical column of about 12.5 microns in diameter, the observed order of convergence of the GCI analysis demonstrates a comparatively negligible dependence of the numerical simulation results on the computational grid beyond about half a micron. Moreover, a higher value of the observed order of convergence and smaller GCI error values for the interIsoFoam [5] solver shows a comparatively better capturing of the liquid-gas interface by using geometric fluxing.