Incompressible separated flows simulations with the smoothed particle hydrodynamics gridless method

Abstract

SUMMARYThe gridless Lagrangian method smoothed particle hydrodynamics (SPH) is preferentially used in CFD to simulate complex ows with one or several convoluted free surfaces. Indeed, this type of ow would require distorted meshes with Lagrangian ÿnite di erence methods or very ÿne meshes with VOF. As the literature is quite scarce concerning SPH validations for academic problems, we present in this paper some results relative to laminar recirculating ows. The ability of SPH to reproduce recirculation zone is revealed through a 2D hill and a backward-facing step geometry: axial velocity proÿles obtained with SPH are quite satisfactory and separation and reattachment points are well predicted in both cases. Moreover, some practical and robust wall modelling conditions are also introduced and the limitation of the nearly incompressible assumption, used in most standard SPH codes, is illustrated. Indeed, we reveal that it is necessary to consider a relatively high speed of sound in order to avoid numerical voids.

Comparisons of weakly compressible and truly incompressible algorithms for the SPH mesh free particle method

“…In terms of SPH parameters, a fourth order of kernel [15] with a smoothing length ratio h/dr of 1.3 is used in both WCSPH and ISPH. The numerical speed of sound in WCSPH is set at c 0 = 100 U Lid instead of the normal definition of speed of sound c 0 = 10U Lid in order to cure the appearance of a void at the center of the cavity; this phenomenon having already been reported in [8]. In the following simulations, dummy particles are involved in the Laplacian operator.…”

Incompressible smoothed particle hydrodynamics

“…For a recent example illustrating these difficulties see Ref. [3]. In addition, the compressibility of the model poses problems with the sound wave reflection at boundaries.…”

Numerical Simulation of Hydrodynamics and Reaeration over a Stepped Spillway by the SPH Method

“…The assumed "reference pressure B" is used to solve the pressure field distribution and ensure both the compressibility of the flow field and the uniformity of particle distribution. In the initial conditions, c 0w can be calculated as follow [27]:…”