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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. [ABSTRACT FROM AUTHOR]