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Title: A comparative study of Rosenbrock-type and implicit Runge-Kutta time integration for discontinuous Galerkin method for unsteady 3D compressible Navier-Stokes equations

Journal Article · · Communications in Computational Physics
 [1];  [2];  [1];  [1]
  1. North Carolina State Univ., Raleigh, NC (United States)
  2. Idaho National Lab. (INL), Idaho Falls, ID (United States)
+ Show Author Affiliations

A comparative study of two classes of third-order implicit time integration schemes is presented for a third-order hierarchical WENO reconstructed discontinuous Galerkin (rDG) method to solve the 3D unsteady compressible Navier-Stokes equations: — 1) the explicit first stage, single diagonally implicit Runge-Kutta (ESDIRK3) scheme, and 2) the Rosenbrock-Wanner (ROW) schemes based on the differential algebraic equations (DAEs) of Index-2. Compared with the ESDIRK3 scheme, a remarkable feature of the ROW schemes is that, they only require one approximate Jacobian matrix calculation every time step, thus considerably reducing the overall computational cost. A variety of test cases, ranging from inviscid flows to DNS of turbulent flows, are presented to assess the performance of these schemes. Here, numerical experiments demonstrate that the third-order ROW scheme for the DAEs of index-2 can not only achieve the designed formal order of temporal convergence accuracy in a benchmark test, but also require significantly less computing time than its ESDIRK3 counterpart to converge to the same level of discretization errors in all of the flow simulations in this study, indicating that the ROW methods provide an attractive alternative for the higher-order time-accurate integration of the unsteady compressible Navier-Stokes equations.

Research Organization:
Idaho National Lab., Idaho Falls, ID (United States)
Sponsoring Organization:
USDOE Office of Nuclear Energy (NE)
Grant/Contract Number:
AC07-05ID14517
OSTI ID:
1357433
Report Number(s):
INL/JOU-15-36158; applab; PII: S1815240616001067
Journal Information:
Communications in Computational Physics, Vol. 20, Issue 04; ISSN 1815-2406
Publisher:
Global Science PressCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 20 works
Citation information provided by
Web of Science

References (34)

Reynolds number and end‐wall effects on a lid‐driven cavity flow journal February 1989
Space–time discontinuous Galerkin method for advection–diffusion problems on time-dependent domains journal December 2006
A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier–Stokes Equations journal March 1997
Very high order PNPM schemes on unstructured meshes for the resistive relativistic MHD equations journal October 2009
A Discontinuous Galerkin Method for the Viscous MHD Equations journal July 1999
A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids journal July 2014
A reconstructed discontinuous Galerkin method for the compressible Navier–Stokes equations on arbitrary grids journal September 2010
A Parallel, Reconstructed Discontinuous Galerkin Method for the Compressible Flows on Arbitrary Grids journal February 2011
An Efficient Implicit Discontinuous Spectral Galerkin Method journal September 2001
A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes journal September 2008
A reconstructed discontinuous Galerkin method based on a Hierarchical WENO reconstruction for compressible flows on tetrahedral grids journal March 2013
A Hermite WENO reconstruction-based discontinuous Galerkin method for the Euler equations on tetrahedral grids journal June 2012
A class of hybrid DG/FV methods for conservation laws II: Two-dimensional cases journal February 2012
Stability analysis of the cell centered finite-volume Muscl method on unstructured grids journal June 2009
A Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids journal November 2012
Implicit solution of the unsteady Euler equations for high-order accurate discontinuous Galerkin discretizations journal August 2007
A dynamic mixed subgrid‐scale model and its application to turbulent recirculating flows journal December 1993
Implicit Large Eddy Simulation of transition to turbulence at low Reynolds numbers using a Discontinuous Galerkin method journal October 2010
High-Order Accurate Discontinuous Finite Element Solution of the 2D Euler Equations journal December 1997
An implicit Hermite WENO reconstruction-based discontinuous Galerkin method on tetrahedral grids journal June 2014
A comparison of vortex and pseudo-spectral methods for the simulation of periodic vortical flows at high Reynolds numbers journal April 2011
Linearly implicit Rosenbrock-type Runge–Kutta schemes applied to the Discontinuous Galerkin solution of compressible and incompressible unsteady flows journal September 2015
Arbitrary high order PNPM schemes on unstructured meshes for the compressible Navier–Stokes equations journal January 2010
Implicit Time Integration Schemes for the Unsteady Compressible Navier–Stokes Equations: Laminar Flow journal June 2002
A discontinuous Galerkin method based on a Taylor basis for the compressible flows on arbitrary grids journal October 2008
A class of hybrid DG/FV methods for conservation laws I: Basic formulation and one-dimensional systems journal February 2012
A Comparative Study of Different Reconstruction Schemes for a Reconstructed Discontinuous Galerkin Method on Arbitrary Grids conference June 2012
A Parallel, Implicit Reconstructed Discontinuous Galerkin Method for the Compressible Flows on 3D Arbitrary Grids conference June 2013
A New Stiffly Accurate Rosenbrock-Wanner Method for Solving the Incompressible Navier-Stokes Equations book January 2013
An Implicit Reconstructed Discontinuous Galerkin Method Based on Automatic Differentiation for the Navier-Stokes Equations on Tetrahedron Grids
  • Xia, Yidong; Luo, Hong; Nourgaliev, Robert
  • 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition https://doi.org/10.2514/6.2013-687
conference January 2013
An implicit, reconstructed discontinuous Galerkin method for the unsteady compressible Navier-Stokes equations on 3D hybrid grids conference June 2014
Preconditioning for modal discontinuous Galerkin methods for unsteady 3D Navier–Stokes equations journal May 2013
Simulation of the Compressible Taylor Green Vortex using High-Order Flux Reconstruction Schemes conference June 2014
A Discontinuous Galerkin Method for Diffusion Based on Recovery conference June 2012

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High-Order Hyperbolic Navier-Stokes Reconstructed Discontinuous Galerkin Method for Unsteady Flows conference June 2019

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Related Subjects

97 MATHEMATICS AND COMPUTING
discontinuous Galerkin
implicit time integration
Navier-Stokes
Rosenbrock-Wanner
WENO