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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

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.
 [1] ;  [2] ;  [1] ;  [1]
  1. North Carolina State Univ., Raleigh, NC (United States)
  2. Idaho National Lab. (INL), Idaho Falls, ID (United States)
Publication Date:
Report Number(s):
Journal ID: ISSN 1815-2406; applab; PII: S1815240616001067
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Communications in Computational Physics
Additional Journal Information:
Journal Volume: 20; Journal Issue: 04; Journal ID: ISSN 1815-2406
Global Science Press
Research Org:
Idaho National Lab., Idaho Falls, ID (United States)
Sponsoring Org:
USDOE Office of Nuclear Energy (NE)
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING; discontinuous Galerkin; implicit time integration; Navier-Stokes; Rosenbrock-Wanner; WENO
OSTI Identifier: