An adaptive meshfree solver for incompressible flows

Abstract

Meshfree methods are particularly suitable for problems involving moving interfaces and adaptive refinement as potentially expensive re-meshing is avoided. Despite this advantage, in the context of incompressible flow, meshfree methods are still plagued by a number of issues including grid degradation accompanying large fluid deformations, large stencil requirements, lack of consistency and conservation, restrictive time steps due to explicit weakly compressible fluid models used, and inability to resolve small spatial scales due to grid uniformity. To address a number of these limitations, we develop a consistent, semi-implicit, adaptive meshfree solver based on the arbitrary Lagrangian-Eulerian (ALE) formulation of the incompressible Navier-Stokes equations. The utility of this meshfree ALE approach will be demonstrated by simulating viscous incompressible flow phenomena around complex moving interfaces through a range of Reynolds numbers.