2020/10/26 by Modesar Shakoor, Shakoor, Modesar, Chung Hae Park +1
Engineering · #Lattice Boltzmann Simulation Studies #Advanced Numerical Methods in Computational Mathematics #Fluid Dynamics and Heat Transfer
paper · pdf · doi:10.48550/arxiv.2010.13716
A novel finite element framework is proposed for the numerical simulation of\ntwo phase flows with surface tension. The Level-Set (LS) method with piece-wise\nquadratic (P2) interpolation for the liquid-gas interface is used in order to\nreach higher-order convergence rates in regions with smooth interface. A\nbalanced-force implementation of the continuum surface force model is used to\ntake into account the surface tension and to solve static problems as\naccurately as possible. Given that this requires a balance between the\ndiscretization used for the LS function, and that used for the pressure field,\nan equal-order P2/P2/P2 scheme is proposed for the Navier-Stokes and LS\nadvection equations, which are strongly coupled with each other. This fully\nimplicit formulation is stabilized using the residual-based variational\nmultiscale framework. In order to improve the accuracy and obtain optimal\nconvergence rates with a minimum number of elements, an anisotropic mesh\nadaption method is proposed where the unstructured mesh is kept as fine as\npossible close to the zero iso-value of the P2 LS function. Elements are\nautomatically stretched in regions with flat interface in order to keep the\ncomplexity fixed during the simulation. The accuracy and efficiency of this\napproach are demonstrated for two and three dimensional simulations of a rising\nbubble.\n