An ALE particle method using upwind interpolation

In the present paper, an ALE particle method is presented for the numerical simulation of incompressible viscous flows. The present approach interpolates physical quantities, e.g., velocity and temperature, using an upwind scheme at an arbitrary new position. In the present approach, the incompressible Navier–Stokes equations are first solved in a Lagrangian step by a least squares moving particle semi-implicit (LSMPS) method. A redistribution of particle positions is then performed in order to deal with the distorted distribution of particles due to the Lagrangian movement. Finally, the particle velocity is interpolated at the particles’ new position, which is computed by two redistribution models. Taylor–Green vortices, lid-driven flows in a cavity and buoyancy-driven flows in a cavity for several Reynolds and Rayleigh numbers are computed as numerical examples. The results are compared with those of similar approaches proposed previously, such as non-upwind interpolation and the meshless advection using a flow-directional local-grid (MAFL) method. The method presented herein exhibits advantages such as higher accuracy and enhanced numerical stability.