This work presents and compares efficient implementations of high-order discontinuous Galerkin methods: a modal matrix-free discontinuous Galerkin (DG) method, a hybridizable discontinuous Galerkin (HDG) method, and a primal formulation of HDG, applied to the implicit solution of unsteady compressible flows. The matrix-free implementation allows for a reduction of the memory footprint of the solver when dealing with implicit time-accurate discretizations. HDG reduces the number of globally-coupled degrees of freedom relative to DG, at high order, by statically condensing element-interior degrees of freedom from the system in favor of face unknowns. The primal formulation further reduces the element-interior degrees of freedom by eliminating the gradient as a separate unknown. This paper introduces a p-multigrid preconditioner implementation for these discretizations and presents results for various flow problems. Benefits of the p-multigrid strategy relative to simpler, less expensive, preconditioners are observed for stiff systems, such as those arising from low-Mach number flows at high-order approximation. The p-multigrid preconditioner also shows excellent scalability for parallel computations. Additional savings in both speed and memory occur with a matrix-free/reduced version of the preconditioner.

Efficient discontinuous Galerkin implementations and preconditioners for implicit unsteady compressible flow simulations / Franciolini, M.; Fidkowski, K. J.; Crivellini, A.. - In: COMPUTERS & FLUIDS. - ISSN 0045-7930. - 203:(2020), p. 104542. [10.1016/j.compfluid.2020.104542]

Efficient discontinuous Galerkin implementations and preconditioners for implicit unsteady compressible flow simulations

Crivellini A.
2020-01-01

Abstract

This work presents and compares efficient implementations of high-order discontinuous Galerkin methods: a modal matrix-free discontinuous Galerkin (DG) method, a hybridizable discontinuous Galerkin (HDG) method, and a primal formulation of HDG, applied to the implicit solution of unsteady compressible flows. The matrix-free implementation allows for a reduction of the memory footprint of the solver when dealing with implicit time-accurate discretizations. HDG reduces the number of globally-coupled degrees of freedom relative to DG, at high order, by statically condensing element-interior degrees of freedom from the system in favor of face unknowns. The primal formulation further reduces the element-interior degrees of freedom by eliminating the gradient as a separate unknown. This paper introduces a p-multigrid preconditioner implementation for these discretizations and presents results for various flow problems. Benefits of the p-multigrid strategy relative to simpler, less expensive, preconditioners are observed for stiff systems, such as those arising from low-Mach number flows at high-order approximation. The p-multigrid preconditioner also shows excellent scalability for parallel computations. Additional savings in both speed and memory occur with a matrix-free/reduced version of the preconditioner.
2020
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/282554
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