Explicit High-Order Discontinuous Galerkin Spectral Element Methods for LES and DNS

Beck, Andrea; Bolemann, Thomas; Hitz, Timon; Mayer, Valentin; Munz, Claus‐Dieter

doi:10.1007/978-3-319-22997-3_17

Cited by 2 publications

(2 citation statements)

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“…Furthermore, these large linear systems often have a saddle-point structure, resulting in poor performance of iterative linear solvers. 6 For example, the local DG discretization of the Poisson problem (5) gives rise to a linear system of the form…”

Section: Iiia Approximation Of Second-order Termsmentioning

confidence: 99%

“…8,9 In recent years, there has been considerable interest in the application of DG to computational fluid dynamics problems, including direct numerical simulation (DNS) and large eddy simulation (LES). 5,23,24 An important advantage of the DG method is the ability to use arbitrary-degree polynomial functions, and thus obtain arbitrarily high spatial order of accuracy. However, the use of high-degree polynomials results in a CFL stability condition that can render explicit time stepping methods impractical, motivating the use of implicit solvers.…”

Section: Introductionmentioning

confidence: 99%

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Interior penalty tensor-product preconditioners for high-order discontinuous Galerkin discretizations

Pazner

Persson

2018

2018 AIAA Aerospace Sciences Meeting

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In this paper, we introduce an interior penalty tensor-product preconditioner for the implicit time integration of discontinuous Galerkin discretizations of partial differential equations with second-order spatial derivatives. This preconditioner can be efficiently formed using a sum-factorized Lanczos algorithm for computing the Kronecker-product singular value decomposition of the diagonal blocks of the Jacobian matrix, and can be applied efficiently using a simultaneous triangularization procedure. In two spatial dimensions, the computational complexity for the overall method is linear per degree of freedom, which is the same as that of a sum-factorized explicit method. This preconditioner exactly reproduces the block Jacobi preconditioner for certain special cases, and compares favorably with the block Jacobi preconditioner for a range of test problems, including viscous compressible flow over a circular cylinder. This preconditioner shows greatly improved performance when compared with a Kronecker-product preconditioner that only incorporates first-order terms.

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Section: Iiia Approximation Of Second-order Termsmentioning

confidence: 99%