skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Authors:
; ; ;
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1413792
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Computers and Fluids
Additional Journal Information:
Journal Volume: 152; Journal Issue: C; Related Information: CHORUS Timestamp: 2017-12-17 18:11:47; Journal ID: ISSN 0045-7930
Publisher:
Elsevier
Country of Publication:
United Kingdom
Language:
English

Citation Formats

Liu, Xiaodong, Xuan, Lijun, Xia, Yidong, and Luo, Hong. A reconstructed discontinuous Galerkin method for the compressible Navier-Stokes equations on three-dimensional hybrid grids. United Kingdom: N. p., 2017. Web. doi:10.1016/j.compfluid.2017.04.027.
Liu, Xiaodong, Xuan, Lijun, Xia, Yidong, & Luo, Hong. A reconstructed discontinuous Galerkin method for the compressible Navier-Stokes equations on three-dimensional hybrid grids. United Kingdom. doi:10.1016/j.compfluid.2017.04.027.
Liu, Xiaodong, Xuan, Lijun, Xia, Yidong, and Luo, Hong. Sat . "A reconstructed discontinuous Galerkin method for the compressible Navier-Stokes equations on three-dimensional hybrid grids". United Kingdom. doi:10.1016/j.compfluid.2017.04.027.
@article{osti_1413792,
title = {A reconstructed discontinuous Galerkin method for the compressible Navier-Stokes equations on three-dimensional hybrid grids},
author = {Liu, Xiaodong and Xuan, Lijun and Xia, Yidong and Luo, Hong},
abstractNote = {},
doi = {10.1016/j.compfluid.2017.04.027},
journal = {Computers and Fluids},
number = C,
volume = 152,
place = {United Kingdom},
year = {Sat Jul 01 00:00:00 EDT 2017},
month = {Sat Jul 01 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/j.compfluid.2017.04.027

Citation Metrics:
Cited by: 4works
Citation information provided by
Web of Science

Save / Share:
  • A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier–Stokes equations on arbitrary grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier–Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need tomore » judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on arbitrary grids. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG method is able to deliver the same accuracy as the well-known Bassi–Rebay II scheme, at a half of its computing costs for the discretization of the viscous fluxes in the Navier–Stokes equations, clearly demonstrating its superior performance over the existing DG methods for solving the compressible Navier–Stokes equations.« less
  • 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,more » and robustness. 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 large eddy simulation (LES) and direct numerical simulation (DNS) of compressible turbulent flows.« less
  • A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need tomore » judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on arbitrary grids. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG method is able to deliver the same accuracy as the well-known Bassi-Rebay II scheme, at a half of its computing costs for the discretization of the viscous fluxes in the Navier-Stokes equations, clearly demonstrating its superior performance over the existing DG methods for solving the compressible Navier-Stokes equations.« less
  • A set of implicit methods are proposed for a third-order hierarchical WENO reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids. An attractive feature in these methods are the application of the Jacobian matrix based on the P1 element approximation, resulting in a huge reduction of memory requirement compared with DG (P2). Also, three approaches -- analytical derivation, divided differencing, and automatic differentiation (AD) are presented to construct the Jacobian matrix respectively, where the AD approach shows the best robustness. A variety of compressible flow problems are computed to demonstrate the fast convergence property of the implemented flowmore » solver. Furthermore, an SPMD (single program, multiple data) programming paradigm based on MPI is proposed to achieve parallelism. The numerical results on complex geometries indicate that this low-storage implicit method can provide a viable and attractive DG solution for complicated flows of practical importance.« less
  • 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,more » 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.« less