A parallel discontinuous Galerkin code based on a Taylor series basis for the compressible Euler equations on unstructured meshes is presented. The parallel numerical method is capable to efficiently simulate the flow physics of the problems considered, including subsonic and transonic compressible inviscid fluid flows around two well known benchmark airfoils. The parallel discontinuous Galerkin method is presented for distributed memory parallel computing architectures, specifically considered cost effective compute clusters, composed of mass-market-commodity-off-the-shelf (M2COTS) computer hardware components interconnected via Ethernet. The parallelization is based on computational domain partitioning, making use of the well-known graph and mesh partitioning package METIS. Single Program Multiple Data (SPMD) message passing parallel programming model has been employed, by making use of the de-facto industry standard Message Passing Interface (MPI) library. Favorable parallelization characteristics of the discontinuous Galerkin scheme have been exploited for hiding the communications behind the computations. The parallel performance of the developed code on an Ethernet based cluster, in terms of speedup is demonstrated.