Unified semi‐analytical wall boundary conditions for inviscid, laminar or turbulent flows in the meshless SPH method

TLDR

Wall boundary conditions in smoothed particle hydrodynamics (SPH) are a key challenge for accurate simulations. The authors propose a new approach that uses a renormalising factor to express all boundary terms. This factor, which depends on wall shape and particle position, is solved via a dynamic equation, replacing ghost particles and improving pressure, friction, and turbulence handling, and is benchmarked against finite‑volume and volume‑of‑fluid schemes. The model yields significantly better wall treatment, as shown by improved hydrostatic tank and dam‑break simulations, accurate velocity profiles in a laminar channel matching theory, and realistic velocity and turbulent viscosity fields in a fish‑pass compared with mesh‑based codes. © 2012 John Wiley & Sons, Ltd.

Abstract

SUMMARY Wall boundary conditions in smoothed particle hydrodynamics (SPH) is a key issue to perform accurate simulations. We propose here a new approach based on a renormalising factor for writing all boundary terms. This factor depends on the local shape of a wall and on the position of a particle relative to the wall, which is described by segments (in two‐dimensions), instead of the cumbersome fictitious or ghost particles used in most existing SPH models. By solving a dynamic equation for the renormalising factor, we significantly improve traditional wall treatment in SPH, for pressure forces, wall friction and turbulent conditions. The new model is demonstrated for cases including hydrostatic conditions for still water in a tank of complex geometry and a dam break over triangular bed profile with sharp angle where significant improved behaviour is obtained in comparison with the conventional boundary techniques. The latter case is also compared with a finite volume and volume‐of‐fluid scheme. The performance of the model for a two‐dimensional laminar flow in a channel is demonstrated where the profiles of velocity are in agreement with the theoretical ones, demonstrating that the derived wall shear stress balances the pressure gradient. Finally, the performance of the model is demonstrated for flow in a schematic fish pass where both the velocity field and turbulent viscosity fields are satisfactorily reproduced compared with mesh‐based codes. Copyright © 2012 John Wiley & Sons, Ltd.