Large-Scale Water Flow Simulation in Mathematica Computing Environment with a PC Cluster
Panjit Musik, Krisanadej Jaroensutasinee · 2022
This work presents a large scale water flow simulation using the lattice Boltzmann method (LBM) with a parallel computation extension for the two dimensional cavity flow simulation. A nine-velocity square lattice model (D2Q9 Model) is used in the LBM simulation. The LBM is an extension of the lattice gas algorithms and approximates the Navier-Stoke equations on a Cellular Automata (CA). A CA was programmed in Mathematica computing environment defining with the 6 CA rules, which were in terms of the particle distribution function. Each of the rules operates on the cells using the information in a Moore neighborhood, which consist of the surrounding nine cells. Parallelization is achieved by using horizontal domain decomposition while each decomposed domain is computed on each nodes of our WAC16P4 Cluster composed on 16 Pentium 4 personal computers. The parallel program is written in Mathematica and parallel computation is done with the Parallel Computing Toolkit. We also invent a new way of communicating necessary information with adjacent slave processors via the Server Message Block (SMB) protocol. Exact simulation results as a small scale simulation, which are comparable to those of previous work, are obtained. With our current tools, it is possible to model large scale computation (e.g. 1000x1000 or 2000x2000 lattice sizes) with less calculation time through our new parallelisation scheme.