CIVA (Cubic Interpolation with Volume/Area Coordinates) and AMR (Adaptive Mesh Refinement) Method for Discrete Boltzmann Equation

Abstract

In recent years, the Lattice Boltzmann Method (LBM) has been developed as an alternative numerical approach in Computational Fluid Dynamics (CFD). In particular, this method is promising for simulations of multiphase and multi component fluid flow involving complex interfacial dynamics. Unlike the conventional CFD methods based on NS equations, the LBM is based on the mesoscopic particle’s kinetic equation. This method has some advantages such as the simplicity of the algorithm (high efficiency on parallel processing), flexible reproduction of interfaces between phases. The conventional LBM, however, requires regular structured grids. But, for complex flow field, unstructured grids should be used. In this study, we describe a computational scheme based on two-dimensional unstructured grids using Cubic Interpolation with Volume/Area coordinates (CIVA) method and Adaptive Mesh Refinement method. As examples of tests of this scheme, single and two-phase flow simulations are presented.