A High Performance Computing approach to the simulation of dense particulate flow using Smoothed Particle Hydrodynamics and Discrete Element Method

摘要

This contribution concentrates on the direct numerical simulation of dense particulate flows. The approach adopted solves the Navier-Stokes equations in conjunction with the Newton-Euler equations of motion associated with the dynamics of the rigid bodies; i.e., the motion of the embedded rigid particles. The simulation of the fluid flow and Fluid Solid Interaction (FSI) phenomena rely on the Smoothed Particle Hydrodynamics (SPH) method. The rigid-body to rigid-body interactions are captured using a Discrete Element Method (DEM) technique, which draws on a visco-elastic model for the mutual frictional-contact interaction. The choice of SPH for the current problem is justified on two grounds.First, it is a Lagrangian method that allows a relatively straightforward modeling of the moving boundaries as well as free surface flow.Second, it is suited for parallel implementation on inexpensive hardware accelerators; i.e., Graphics Processing Unit (GPU) cards, thus allowing for the simulation of complex flow scenarios.While the flow simulation using basic SPH models is generally second order accurate, the pressure field may still exhibits large oscillation.One of the most straightforward and computationally inexpensive solution to this problem is the density re-initialization technique.Additionally, to prevent particles interpenetration and improve the incompressibility of the flow field, the XSPH correction is adopted herein. The accuracy of the simulation engine is benchmarked against a transient Poiseuille flow for which an analytical solution is available. The Lagrangian, particle-based, modeling of the fluid allows a fairly straightforward FSI simulation via the spherical decomposition of the rigid particles surface. This technique is used in the simulation and validation of lateral migration of cylindrical objects in Poiseuille flow, which is associated with the Segre-Silberberg effect.Preliminary results show the capability of the aforementioned algorithm to simulate the dilute particulate flow in an arbitrarily shaped medium, a scenario relevant in microbiology related applications.Despite being relatively straightforward to implement for the analysis of both internal as well as free surface flows, a na飗e SPH simulation does not exhibit the efficiency required for the 3D simulation of real-life fluid flow problems. To address this issue, the software implementation of the proposed method uses a scalable spatial subdivision of the flow field that allows for an efficient 3D simulation of the particulate flow.Preliminary numerical experiments demonstrate linear time scaling with respect to the problem size; i.e., number of fluid discretization particles. The overall simulation algorithm was implemented in parallel and on the GPU to simulate the fluid flow over a granular bed. The resulting simulation capability will be instrumental in simulating real-life problems in bioenginering and polymer science.