A super-parallel mixed explicit discontinuous Galerkin method for the second-order Boltzmann-based constitutive models of rarefied and microscale gases

• Published in: Computers & fluids 2017-11, Vol.157, p.146-163
• Main Authors: Raj, L. Prince, Singh, S., Karchani, A., Myong, R.S.
• Format: Article
• Language: English
• Subjects: Computational efficiency; Computational fluid dynamics; Conservation laws; Constitutive equations; Constitutive models; Discontinuous Galerkin (DG); Finite volume method; Galerkin method; Mathematical models; Navier-Stokes equations; Nonlinear coupled constitutive relations; Parallel processing; Plate cylinders; Plates (structural members); Rarefied and microscale gases; Solvers; Super-parallel performance
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2017.08.026

•A super-parallel DG solver for the second-order constitutive models of rarefied and microscale gases is developed.•Parallel implementation of a mixed DG method is achieved for triangular meshes.•Computational cost of the serial and parallel solvers is investigated for various rarefied and microscale conditions.•Super-parallel performance of the second-order algebraic NCCR model is reported for the first time. Super-parallel performance of a mixed explicit discontinuous Galerkin method is reported for the second-order Boltzmann-based nonlinear coupled constitutive models of rarefied and microscale gases. One of the challenging issues in the discontinuous Galerkin (DG) method is the higher computational cost compared with the traditional finite volume method (FVM) for a given set of grids. In the present study, we focus on the computational cost of a mixed modal explicit DG method for solving the conservation laws in conjunction with the first- and second-order Boltzmann-based constitutive models, in particular, in the context of parallelization of the implicit algebraic constitutive equations of rarefied and microscale gases in continuum and transition regimes. The computational cost of the Navier-Stokes-Fourier (NSF) and nonlinear coupled constitutive relation (NCCR) solvers is investigated in the serial and parallel frameworks. It was shown that the computational cost of the NCCR solver behaves nonlinearly with respect to the number of elements, due to the dependence of the number of iterations of the NCCR solver on the flow structure and the degree of thermal non-equilibrium. Such nonlinear dependence was clearly demonstrated from numerical solutions of three representative flows; flat plate, cylinder, and wedge. Ultimately, this nonlinear behavior of computational cost associated with nonlinear performance of the DG-NCCR solver resulted in an unexpected super-parallel performance in parallel processing.