Building a numerical framework to model gas-liquid-solid interactions using meshfree interpolation methods

Abstract

In this work, we present a numerical framework that can model and simulate gas-liquid-solid three-phase interactions. A non-boundary-fitted approach is developed to simultaneously accommodate the moving gas-liquid interfaces and deforming solid. The connectivity-free front tracking method (CFFT) is adopted to track the gas-liquid interface, where an approximation-correction step is used to construct an indicator field without requiring the connectivity of the interfacial points. Therefore, topological change such as free surfaces with bubble breaking up and coalescing can be handled more easily and robustly. The fluid-solid interactions are modeled using the modified immersed finite element method (mIFEM). A more realistic and accurate solid movement and deformation are achieved by solving the solid dynamics, rather than been imposed as in the original IFEM. The coupling of the two algorithms is achieved using a meshfree interpolation function, the reproducing kernel particle method. The concept of constructing the indicator function to distinguish gas from liquid and fluid from solid naturally combines the CFFT and mIFEM algorithms together, and simulate the complex 3-phase physical system in a cohesive manner.