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AHPCRC Bulletin: Winter/Spring 1996 - Volume 6 Number 1-2

Fluid-Particle Simulations Reaching 100 Particles

Andrew Johnson and Tayfun Tezduyar (AHPCRC-UM)

We have developed a new high performance computing tool for 3D simulation of fluid-particle interactions with the number of particles reaching 100. The mathematical modeling is based on the time-dependent Navier-Stokes equations governing the flow around the particles and Newton's law of motion governing the 3D dynamics of the particles with the fluid forces acting on these particles calculated from the flow field. In developing this tool, we started with the set of methods we developed earlier for simulations involving an order of magnitude less particles (see "Automatic Mesh Generation and Update Strategies in 3D Flow Simulations, AHPCRC Bulletin, Fall 1994-Vol. 4 No. 4) and used some of these methods. Bringing the capability to this level, however, also required introducing new methods developed by taking into consideration issues that we were not so concerned about when the number of particles was much fewer. This tool is capable of keeping the computing durations involved in this class of simulations to acceptable levels.

At the core of this tool are the stabilized space-time finite element formulation for moving boundaries and interfaces and implementation of this formulation on parallel platforms. The surrounding methods include: fast automatic mesh generation with structured layers of elements around particles, a mesh update method based on automatic mesh moving with remeshing only as needed, an efficient method for projecting the solution after each remesh, surface mesh refinement to increase accuracy when two solid surfaces get close, and multi-platform computing with high-speed inter platform communication. In these simulations, while the mesh partitioning, flow computations, and mesh movements are performed on the AHPCRC's 512-node CM-5, the mesh generation and projection is accomplished on the AHPCRC's 20-processor SGI Onyx system. The two platforms communicate via a HiPPI channel.

To test and demonstrate this new capability, we applied it to the simulation of 101 spheres falling in a liquid-filled tube. The spheres, in addition to interacting with the fluid, interact and sometimes collide with each other and with the tube wall. We simulated two cases with 101 spheres: with the size of the spheres random in one case and uniform in the second. In both cases, the simulation is started with the spheres distributed randomly in the tube. The mesh sizes during these simulations reach 1.2 million tetrahedral elements (resulting in approximately 2.6 million coupled, nonlinear equations to be solved at each time step), and the number of time steps is around 800. Figure 1 shows the simulations for both cases, where the approximate, average Reynolds number is 40. These particular simulations are not meant to be in depth studies of this class of fluid-particle interactions but are intended to show how the advanced computational methods developed, together with modern parallel computing platforms, enable us to carry out this difficult class of simulations at levels that would have been unthinkable a few years ago.


Figure 1. Simulations for 101 spheres falling in a liquid-filled tube. The pictures show, at four instants during the simulation, the random-sized spheres in the upper half of the page and the uniform-sized ones in the lower half. The average Reynolds number is approximately 40. The number of time steps for each simulation is around 800, and at each time step approximately 2.6 million coupled, nonlinear equations are solved. The computations are carried out using a multi-platform computing environment, with the AHPCRC's 896-node CM-5 and 20-processor SGI Onyx, and a HiPPI channel between the two.


Figure 2. Simulations for 101 spheres falling in liquid-filled tube. The pictures in the upper part of the page show the random-sized spheres and those in the lower part show the uniform-sized ones. In both cases, the pictures on the left show a sequence of two spheres exhibiting drafting, touching and tumbling, while the picture on the right shows all the spheres, highlighting several pairs of spheres in similar interaction.

This simulation tool can be used to help understand the behavior of fluid-particle mixtures which are used in many practical applications. The methods used in developing this new tool certainly leave room for future enhancements in quite a few directions we can think of (e.g. mesh generation and inter-platform communication), and we plan to pursue those later to further increase the power of this tool which, we think, has just opened a new door to exploring science and technology involving fluid-particle interactions.