High-Order Eulerian Incompressible Smoothed Particle Hydrodynamics with Transition to Lagrangian Free-Surface Motion

摘要

The incompressible Smoothed Particle Hydrodynamics (ISPH)method is derived in Eulerian form with high-order smoothing kernels toprovide increased accuracy for a range of steady and transient internalflows. Periodic transient flows, in particular, demonstrate high-orderconvergence and accuracies approaching, for example, spectral mesh-basedmethods. The improved accuracies are achieved through new high-orderGaussian kernels applied over regular particle distributions with timestepping formally up to 2nd order for transient flows. The approach canbe easily extended to model free surface flows by merging from Eulerianto Lagrangian regions in an Arbitrary-Lagrangian-Eulerian (ALE) fashion,and a demonstration with periodic wave propagation is presented. In thelong term, it is envisaged that the method will greatly increase theaccuracy and efficiency of SPH methods, while retaining the flexibilityof SPH in modelling free surface and multiphase flows.