A consistent and fast weakly compressible smoothed particle hydrodynamics with a new wall boundary condition

Abstract

SUMMARYA modified weakly compressible smoothed particle hydrodynamics (WCSPH) is presented, which utilizes consistent discretization schemes for spatial derivatives in the flow equations. Here, each SPH particle is considered as a computational point that represents a specific part of the fluid. To overcome non-physical oscillations that usually arise in standard WCSPH, we modified the mass conservation equation by using a numerical filter. This modification is based on the difference between two discretization schemes used for the term r rP Á. Furthermore, a new implementation of wall boundary condition in SPH is introduced. This condition is imposed on the pressure of wall boundary particles to ensure that the acceleration of each boundary particle in normal direction to the wall is zero. Thus, no penetration through walls will occur. To examine the performance of the modified method, we solved a series of two-dimensional incompressible internal flow benchmark problems. By comparing the result with analytical solutions and the results of the standard WCSPH, we show that the use of consistent schemes in conjunction with the proposed numerical filter improves both accuracy and speed of the numerical method.

Consistent inlet and outlet boundary conditions for particle methods

“…The reason for using the ALE technique is to maintain a regular particle distribution as well as a high accuracy. This technique has been proved to be successful in a lot of previous works …”

ISPH Modelling and Analysis of Fluid Mixing in a Microchannel with an Oscillating or a Rotating Stirrer

“…Although new semi-analytical approaches to wall boundary conditions are available (Monaco et al, 2011;Fatehi and Manzari, 2011b), the dummy particles theory of Lee et al (2008) has been found to be more compatible for the simulations presented herein. Two layers of dummy particles are arranged close to each wall boundary similar to those particles defined by Lee et al (2008).…”

FPM Simulations of a High-Speed Water Jet Validation with CFD and Experimental Results

“…The approximated function f and the kernel W are expressed as (4) and (5) to simplify the notation. In the present work, the quintic Wendland kernel (6) used by Fatehi and Manzari [10] …”

“…The damping of the spurious oscillation in the pressure field proposed by Fatehi and Manzari [10] is applied to (17). The terms (19) and (20) represent two different formulations for the approximation of the Laplacian of the pressure.…”

“…In the present study, the FPM kernel from Fang et al [9] is used to improve the consistency of the standard SPH. The numerical oscillations are reduced by the mass equation correction proposed by Fatehi and Manzari [10]. Finally, the temporal integration scheme of Molteni and Colagrossi [11] is implemented to increase the overall accuracy and stability of the simulations.…”