Direct Simulation of Lateral Migration of Buoyant Particles in Channel Flow Using GPU Computing

The current work promotes the implementation of the Smoothed Particle Hydrodynamics (SPH) method for the Fluid-Solid Interaction (FSI) problems on three levels: 1- an algorithm is described to simulate FSI problems, 2- a parallel GPU implementation is described to efficiently alleviate the performance problem of the SPH method, and 3- validations against other numerical methods and experimental results are presented to demonstrate the accuracy of SPH and SPH-based FSI simulations. While the numerical solution of the fluid dynamics is performed via SPH method, the general Newton-Euler equations of motion are solved for the time evolution of the rigid bodies. Moreover, the frictional contacts in the solid phase are resolved by the Discrete Element Method (DEM), which draws on a viscoelastic model for the mutual interactions. SPH is a Lagrangian method and allows an efficient and straightforward coupling of the fluid and solid phases, where any interface, including boundaries, can be decomposed by SPH particles. Therefore, with a single SPH algorithm, fluid flow and interfacial interactions, namely force and motion, are considered. Furthermore, without any extra effort, the contact resolution of rigid bodies with complex geometries benefits from the spherical decomposition of solid surfaces. Although SPH provides 2nd order accuracy in the discretization of mass and momentum equations, the pressure field may still exhibit large oscillations. One of the most straightforward and computationally inexpensive solutions to this problem is the density re-initialization technique. Additionally, to prevent particle interpenetration and improve the incompressibility of the flow field, the XSPH correction is adopted herein. Despite being relatively straightforward to implement for the analysis of both internal and free surface flows, a naïve 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 framework relies on parallel implementation of the spatial subdivision method on the Graphics Processing Unit (GPU), which allows for an efficient 3D simulation of the fluid flow. Similarly, the time evolution and contact resolution of rigid bodies are implemented using independent GPU-based kernels, which results in an embarrassingly parallel algorithm. Three problems are considered in the current work to show the accuracy of SPH and FSI algorithms. In the first problem, the simulation of the transient Poiseuille flow exhibits an exact match with the analytical solution in series form. The lateral migration of the neutrally buoyant circular cylinder, referred to as tubular pinch effect, is successfully captured in the second problem. In the third problem, the migration of spherical particles in pipe flow was simulated. Two tests were performed to demonstrate whether the Magnus effect or the curvature of the velocity profile cause the particle migration. At the end, the original experiment of the Segre and Silberberg (Segre and Silberberg, Nature 189 (1961) 209–210), which is composed of 3D fluid flow and several rigid particles, is simulated.