Optimizing the Parallel Granular Gas Solver to study the crater formation

Applicant

Prof. Dr. Thorsten Pöschel
Institute for Multiscale Simulation
Friedrich-Alexander Universität Erlangen-Nürnberg

Project Summary

The moving sand dunes, avalanches and the dense planetary rings are granular systems which consists of countless number of particles. The study of such huge systems is impossible with current particle based methods such as Discrete Element Method (DEM) and Event-Driven Molecular Dynamics (EDMD). However, a hydrodynamical (HD) method is a suitable alternative to study these phenomena. The hydrodynamic equations of the granular flow, describes the system by average field variables like particle number density, flow velocity and temperature. The time evolution of these quantities is governed by hydrodynamic equations. The solution to these equations provides valuable information about the granular systems.

We developed a granular flow solver that is based on C++ and parallelized with MPI standard to solve the hydrodynamic equations of the granular flow. We did several optimizations to increase the performance and parallel efficiency of the Granular Flow Solver. The optimizations include modifying the MPI communication pattern, the inlining of the functions, memory management and eliminating the expensive operations. These optimizations improved the single-core and parallel efficiency of the solver significantly.

Picture shows distribution of particles at 0 seconds, 0.5 seconds and 1.0 seconds for two different methods. The top row shows the individual particles, whereas the bottom row shows only shaded density distributions.At the first time step, the particles are distributed homegenously over the whole domain. At 0.5s, the particles are clustered in the left part of the domain, at 1.0s the particles are clustered even more densely in the right part of the domain.
A qualitative comparison between DEM (top row) and and the HD method (bottom row). Each column shows a snapshots of the density field. The box of size is 2.5 cm by 1.2 cm by 1.2 cm and is initially filled with a homogeneous gas of 0.5 mm particles with packing fraction of 0.32. These patterns are formed when we shake the box with frequency of 20 Hz and Amplitude of 2mm.

The current solver is a powerful tool to simulate a vast range of systems with various boundary conditions including the shaking boundaries which is widely used in the study of granular materials. Figure 1 shows a comparison between the density field of the HD solver and the well-known DEM simulation. The accuracy and performance of the current solver is benchmarked with different test cases. Despite all the approximations in HD model, all tests show a very good agreement with the particle based simulations.

More details are available in the full-length report: report_poeschel_2018.