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Title: A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids

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 flow 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.
Authors:
 [1] ;  [1] ;  [1] ;  [2]
  1. North Carolina State Univ., Raleigh, NC (United States). Dept. of Mechanical and Aerospace Engineering
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Report Number(s):
INL/JOU-14-31336
Journal ID: ISSN 0045-7930
Grant/Contract Number:
AC07-05ID14517
Type:
Accepted Manuscript
Journal Name:
Computers and Fluids
Additional Journal Information:
Journal Volume: 98; Journal Issue: C; Journal ID: ISSN 0045-7930
Publisher:
Elsevier
Research Org:
Idaho National Lab. (INL), Idaho Falls, ID (United States)
Sponsoring Org:
USDOE Office of Nuclear Energy (NE)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Automatic differentiation; Discontinuous Galerkin; Hierarchical WENO reconstruction; Implicit Methods; Parallel computing
OSTI Identifier:
1177217

Xia, Yidong, Luo, Hong, Frisbey, Megan, and Nourgaliev, Robert. A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids. United States: N. p., Web. doi:10.1016/j.compfluid.2014.01.023.
Xia, Yidong, Luo, Hong, Frisbey, Megan, & Nourgaliev, Robert. A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids. United States. doi:10.1016/j.compfluid.2014.01.023.
Xia, Yidong, Luo, Hong, Frisbey, Megan, and Nourgaliev, Robert. 2014. "A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids". United States. doi:10.1016/j.compfluid.2014.01.023. https://www.osti.gov/servlets/purl/1177217.
@article{osti_1177217,
title = {A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids},
author = {Xia, Yidong and Luo, Hong and Frisbey, Megan and Nourgaliev, Robert},
abstractNote = {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 flow 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.},
doi = {10.1016/j.compfluid.2014.01.023},
journal = {Computers and Fluids},
number = C,
volume = 98,
place = {United States},
year = {2014},
month = {7}
}