Discrete gas-kinetic scheme-based arbitrary Lagrangian–Eulerian method for moving boundary problems

Abstract

In this work, a discrete gas-kinetic scheme (DGKS) based on the arbitrary Lagrangian–Eulerian (ALE) method is proposed for the simulation of moving boundary problems. The governing equations are the ALE-based Navier–Stokes equations, which are discretized using the finite volume method. Starting from a circular function-based Boltzmann equation, a grid motion term is introduced to obtain the Boltzmann equation in ALE form. Based on the moment relations and Chapman–Enskog analysis, the moment of particle velocity and distribution function are summed to obtain the fluxes. The DGKS expression in the ALE framework can then be derived. In this method, the flux at the cell interface can be calculated from the local solution of the Boltzmann equation, which is physically realistic and makes the algorithm more stable. As DGKS is based on a multidimensional particle velocity model, it is not necessary to use approximate values for the reconstruction process. In addition, DGKS can simultaneously handle inviscid and viscous fluxes when simulating viscous flow problems, resulting in a higher degree of consistency. Finally, several moving boundary examples are simulated to validate the ALE-DGKS method. The results show the algorithm was observed to achieve second-order accuracy and can solve moving boundary problems effectively.