A reconstructed discontinuous Galerkin method for the compressible Navier-Stokes equations on three-dimensional hybrid grids

Liu, Xiaodong; Xuan, Lijun; Xia, Yidong; Luo, Hong

doi:10.1016/j.compfluid.2017.04.027

A reconstructed discontinuous Galerkin method for the compressible Navier-Stokes equations on three-dimensional hybrid grids

Journal Article · Tue May 02 00:00:00 EDT 2017 · Computers and Fluids

DOI:https://doi.org/10.1016/j.compfluid.2017.04.027· OSTI ID:1772415

Liu, Xiaodong ^[1]; Xuan, Lijun ^[1]; Xia, Yidong ^[2]; Luo, Hong ^[1]

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

A reconstructed discontinuous Galerkin (rDG(P1P2)) method, originally introduced for the compressible Euler equations, is developed for the solution of the compressible Navier–Stokes equations on 3D hybrid grids. In this method, a piecewise quadratic polynomial solution is obtained from the underlying piecewise linear DG solution using a hierarchical Weighted Essentially Non-Oscillatory (WENO) reconstruction. The reconstructed quadratic polynomial solution is then used for the computation of the inviscid fluxes and the viscous fluxes using the second formulation of Bassi and Reay (Bassi–Rebay II). The developed rDG(P₁P₂) method is used to compute a variety of flow problems to assess its accuracy, efficiency, and robustness. Additionally, the numerical results demonstrate that the rDG(P₁P₂) method is able to achieve the designed third-order of accuracy at a cost slightly higher than its underlying second-order DG method, outperform the third order DG method in terms of both computing costs and storage requirements, and obtain reliable and accurate solutions to the direct numerical simulation (DNS) of compressible turbulent flows.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1772415

Alternate ID(s):: OSTI ID: 1413792

Report Number(s):: LA-UR--19-20828

Journal Information:: Computers and Fluids, Journal Name: Computers and Fluids Vol. 152; ISSN 0045-7930

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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42 ENGINEERING
Compressible Navier-Stokes equation
Discontinuous Galerkin method
Unstructured grids
WENO reconstruction

A reconstructed discontinuous Galerkin method for the compressible Navier-Stokes equations on three-dimensional hybrid grids

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