A third-order implicit discontinuous Galerkin method based on a Hermite WENO reconstruction for time-accurate solution of the compressible Navier-Stokes equations

Xia, Yidong; Liu, Xiaodong; Luo, Hong; Nourgaliev, Robert

doi:10.1002/fld.4057

A third-order implicit discontinuous Galerkin method based on a Hermite WENO reconstruction for time-accurate solution of the compressible Navier-Stokes equations

Journal Article · Mon Jun 01 00:00:00 EDT 2015 · International Journal for Numerical Methods in Fluids

DOI:https://doi.org/10.1002/fld.4057· OSTI ID:1357240

Xia, Yidong ^[1]; Liu, Xiaodong ^[2]; Luo, Hong ^[2]; Nourgaliev, Robert ^[3]

Idaho National Lab. (INL), Idaho Falls, ID (United States)
North Carolina State Univ., Raleigh, NC (United States)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Here, a space and time third-order discontinuous Galerkin method based on a Hermite weighted essentially non-oscillatory reconstruction is presented for the unsteady compressible Euler and Navier–Stokes equations. At each time step, a lower-upper symmetric Gauss–Seidel preconditioned generalized minimal residual solver is used to solve the systems of linear equations arising from an explicit first stage, single diagonal coefficient, diagonally implicit Runge–Kutta time integration scheme. The performance of the developed method is assessed through a variety of unsteady flow problems. Numerical results indicate that this method is able to deliver the designed third-order accuracy of convergence in both space and time, while requiring remarkably less storage than the standard third-order discontinous Galerkin methods, and less computing time than the lower-order discontinous Galerkin methods to achieve the same level of temporal accuracy for computing unsteady flow problems.

View Accepted Manuscript (DOE)

Research Organization:: Idaho National Lab., Idaho Falls, ID (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC07-05ID14517

OSTI ID:: 1357240

Report Number(s):: INL/JOU--15-35604

Journal Information:: International Journal for Numerical Methods in Fluids, Journal Name: International Journal for Numerical Methods in Fluids Journal Issue: 8 Vol. 79; ISSN 0271-2091

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
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A third-order implicit discontinuous Galerkin method based on a Hermite WENO reconstruction for time-accurate solution of the compressible Navier-Stokes equations

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