An implicit boundary approach for viscous compressible high Reynolds flows using a hybrid remeshed particle hydrodynamics method

Abstract

We present an implicit boundary particle method with background mesh adaptation. We use a Brinkman penalisation to represent the boundary of the domain and a remeshed particle method to simulate viscous flow with high Reynolds numbers. A penalty term is added to the Navier-Stokes equations to impose the boundary conditions. The boundary conditions are enforced to a specific precision with no need to modify the numerical method or change the grid, achieving an implicit approach for flow around complex boundaries/geometries simulation. The main idea of the Brinkman penalisation method is to model the solid obstacle as a porous medium. The governing equations for the compressible fluid and penalised Navier-Stokes for the porous medium are solved simultaneously, without need for interface conditions. The accuracy of the method is tested for a number of benchmark problems starting with simple cases such as a periodic laminar flow in a channel (Poiseuille flow), to more complex problems such as the lid-driven cavity with high Reynolds numbers, the reflection and propagation of a compressible shock wave, and finally swirling flow in a model two-stroke diesel engine. The remeshed particle-mesh method coupled with Brinkman penalisation provides a good quality simulation and the results are in agreement with analytical or reference solutions.