@Article{CiCP-20-1016,
author = {Xiaodong Liu, Yidong Xia, Hong Luo and Lijun Xuan},
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 = {Communications in Computational Physics},
year = {2018},
volume = {20},
number = {4},
pages = {1016--1044},
abstract = {<p style="text-align: justify;">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. 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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.300715.140316a},
url = {http://global-sci.org/intro/article_detail/cicp/11181.html}
}