Abstract
An efficient parallel scheme based on the nodal discontinuous Galerkin finite element method (nodal-DGFEM) for the numerical solution of the partial differential equations governing fluid flow phenomena is discussed. The flow solver is demonstrated to perform numerical simulation of two-dimensional flow regimes on unstructured triangular grids. The parallel implementation serves to fulfill the requisition of the numerical method regarding high-performance computing resources. The distributed memory programming model with the domain decomposition approach is adopted. The message passing interface library is used for communication among the parallel processes, which are assigned domain-decomposed subproblems. The presented parallelization strategy accurately and efficiently tackles the communication of multi-node data on the element edges between the neighboring parallel processes. The efficacy and efficiency of the parallel solver are demonstrated through solving the well-known problem of non-viscous isentropic convecting vortex flow on parallel systems. The parallelization would extend the scope of the DGFEM by producing solutions in reasonable time frames.
Highlights
The simulations of fluid flows frequently require solving partial differential equations (PDEs) numerically
Finite difference methods (FDMs), finite volume methods (FVMs), and finite element methods (FEMs) are conventionally used techniques for the numerical solution of PDEs. There is another class of methods, namely, the discontinuous Galerkin finite element method (DGFEM or DGM), which is a hybrid form of FEM and FVM
The parallel nodal-DGFEM solver is tested on a well-known test case involving the convection of an isentropic vortex in the inviscid flow
Summary
The simulations of fluid flows frequently require solving partial differential equations (PDEs) numerically. Among the high-performance parallel computers, the clusters may present the most cost-efficient solution for the computational fluid dynamics (CFD) applications. They are formed by interconnecting a number of standalone personal computers using some interconnection network. Multicore CPU technology has emerged as the building block of all computer systems, be it a standalone personal computer or the biggest supercomputing machines. All of these parallel scitation.org/journal/adv systems can be used efficiently through distributed memory parallel programming
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