Performance of a Numerical Three-Dimensional Transonic and Supersonic Flow Algorithm Using Finite Elements in a Cluster of Personal Computers

Abstract

The performance of an algorithm to simulate three-dimensional (3-D) high compressible transonic and supersonic flows using the Finite Element Method, which is implemented for distributed memory and hybrid shared-distributed memory parallel configurations in a cluster of personal computers, is presented in this work. An explicit onestep Taylor-Galerkin scheme is used for time integration and both tetrahedral and hexahedral meshes are employed in the spatial discretization. Task division is achieved through a technique based on nodal ordering to obtain two distinct configurations: the first one minimizes the number of neighbor sub-domains in the partitioned mesh, minimizing the number of communication operations among the cluster nodes, and the second one minimizes the number of common elements among sub-domains, minimizing the amount of data exchanged by the cluster nodes through the network. The influence of the meshes size and type (structured or unstructured), the task division employed as well as the number of cores or processors of each cluster node is analyzed through two examples in terms of speed-up and parallel efficiency. The results obtained from these examples show the importance of using a task division suited to the hardware configuration of the cluster in the efficiency of parallel solutions, and the viability of using personal computers in clusters as an alternative to reach relatively high performance computing with cheap resources.