An Innovative MPI Topology for Direct Computational Fluid Dynamic Simulations

Today, parallel programming models (PPM) have secured center-stage in the solution of computational fluid dynamics (CFD) problems. In fact, PPM are implemented in all fields of computer programming where large memory densities and high computational intensities are major requirements. In general, PPM is an abstraction of the parallel computer architecture (PCA) expressed in the form of soft computing. Further, PCA can be divided into two distinct but important sets: the process interaction set, and the problem decomposition set. The problem decomposition set is best defined by the subject matter experts, and as such, will not be explored herein. However, there are many generalities to be had in the process interaction set, as this set is yet to be fully optimized and exploited. In this paper, the process interaction set associated with today’s high-performance computing (HPC) platforms will be discussed. This discussion centers on the optimal arrangements of the soft computing tasks typically implemented in the solution of CFD problems. Of special interest to this work are; the soft computing tasks that require the use of Message Passing Interface (MPI) libraries, and process parallelization strategies (PPS). Further, in this paper, the process interaction sets are discussed in relationship to their applications. In this case, the focus is on the CFD Integra-Differential control volume approach developed by the authors of this paper. It is well-known that CFD approaches employ large matrix operations. Matrix decomposition tasks were greatly improved due to PCA, both in terms of their computational intensity and speed. However, great challenges still remain, when it comes to effectively mapping a given CFD strategy to an existing PCA. If the MPI communicator is considered a group of processes, ranked from 0 to n-1. Then for most CFD problems, a linear arrangement of these processes would not possibly reflect the logic of communication these CFD problems demand. For example, 2D and 3D CFD problems require 2D and 3D grids, and so too, they require 2D and 3D data decomposition, data computations, data transport and data storage. This is where MPI virtual topology and tools presents great opportunities to the CFD community. The topological structure of a HPC network may be depicted physically or logically. MPI topology allows great flexibility for the rearrangement of nodes in a given communication network. A process mapping topology structure to CFD solution procedure can not only effectively improve the communication efficiency of the MPI application and cut down on the execution times, but also easier to program. In the effort proposed herein, a PPM process interaction model will be implementation on a Cartesian grid system to solve the Rayleigh-Taylor Instability (RTI) problem among a few others. These problems will be solved on desktop computer (Mac-mini) with Intel Core^TM i7-8700B and HPC for comparative purposes. The PPM solution for the RTI problem will be discussed alongside benchmark data. Moreover, the results of the PPM with incremental computational density alongside the benchmark data will be compared with the execution times with OpenMP and MPI for multi-thread CPUs.