An arbitrary Lagrangian-Eulerian SPH-MLS method for the computation of compressible viscous flows

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 general formulation that includes some well-known meshfree methods particular case. The is based on use of Moving Least Squares (MLS) approximants weight functions Galerkin and accurate discretize convective viscous fluxes. This also verifies discrete partition unity reproduces zero-gradient condition for constant functions. Convective fluxes are discretized Riemann solvers. order obtain high accuracy MLS used high-order reconstruction states. performance proposed demonstrated by solving different steady unsteady benchmark problems.