An Arbitrary Lagrangian-Eulerian SPH-MLS Method for the Computation of Compressible Viscous Flows

Abstract

[Abstract] In this work we present a high-accurate discretization to solve the compressible Navier-Stokes equations using an Arbitrary Lagrangian-Eulerian meshless method (SPH-MLS), which can be seen as a general formulation that includes some well-known meshfree methods as a particular case. The formulation is based on the use of Moving Least Squares (MLS) approximants as weight functions on a Galerkin formulation and to accurate discretize the convective and viscous fluxes. This formulation also verifies the discrete partition of unity and reproduces the zero-gradient condition for constant functions. Convective fluxes are discretized using Riemann solvers. In order to obtain high accuracy MLS is also used for the high-order reconstruction of the Riemann states. The accuracy and performance of the proposed method is demonstrated by solving different steady and unsteady benchmark problems.