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High order parallelisation of an unstructured grid, discontinuous-Galerkin finite element solver for the Boltzmann–BGK equation

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ABSTRACT This paper outlines the implementation and performance of a parallelisation approach involving partitioning of both physical space and velocity space domains for finite element solution of the Boltzmann-BGK equation.… Click to show full abstract

ABSTRACT This paper outlines the implementation and performance of a parallelisation approach involving partitioning of both physical space and velocity space domains for finite element solution of the Boltzmann-BGK equation. The numerical solver is based on a discontinuous Taylor–Galerkin approach. To the authors' knowledge this is the first time a ‘high order’ parallelisation, or `phase space parallelisation', approach has been attempted in conjunction with a numerical solver of this type. Restrictions on scalability have been overcome with the implementation detailed in this paper. The developed algorithm has major advantages over continuum solvers in applications where strong discontinuities prevail and/or in rarefied flow applications where the Knudsen number is large. Previous work by the authors has outlined the range of applications that this solver is capable of tackling. The paper demonstrates that the high order parallelisation implemented is significantly more effective than previous implementations at exploiting High Performance Computing architectures.

Keywords: finite element; solver; parallelisation; high order; order parallelisation

Journal Title: International Journal of Computational Fluid Dynamics
Year Published: 2019

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