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Title: A high-order discontinuous Galerkin method with unstructured space–time meshes for two-dimensional compressible flows on domains with large deformations

Abstract

We introduce a high-order accurate space-time discontinuous Galerkin method for solving two-dimensional compressible flow problems on fully unstructured space-time meshes. The discretization is based on a nodal formulation, with appropriate numerical fluxes for the first and the second-order terms, respectively. The scheme is implicit, and we solve the resulting non-linear systems using a parallel Newton-Krylov solver. The meshes are produced by a mesh moving technique with element connectivity updates, and the corresponding space-time elements are produced directly based on these local operations. To obtain globally conforming tetrahedral meshes, we first derive the required conditions on a prism boundary mesh to allow for a valid local triangulation. Next, we present an efficient algorithm for finding a global mesh that satisfies these conditions. We additionally show how to add and remove mesh nodes, again using local constructs for the space-time mesh. Our approach is demonstrated on a number of test problems, showing the high-order accuracy for model problems, and the ability to solve flow problems on domains with complex large deformations.

Authors:
 [1];  [1]
  1. Univ. of California, Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1524036
Alternate Identifier(s):
OSTI ID: 1245264
Grant/Contract Number:  
AC02-05CH11231; FA9550-10-1-0229
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Computers and Fluids
Additional Journal Information:
Journal Volume: 118; Journal Issue: C; Journal ID: ISSN 0045-7930
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; discontinuous Galerkin; space-time; high-order accuracy; deformable domains; Navier-Stokes

Citation Formats

Wang, Luming, and Persson, Per-Olof. A high-order discontinuous Galerkin method with unstructured space–time meshes for two-dimensional compressible flows on domains with large deformations. United States: N. p., 2015. Web. doi:10.1016/j.compfluid.2015.05.026.
Wang, Luming, & Persson, Per-Olof. A high-order discontinuous Galerkin method with unstructured space–time meshes for two-dimensional compressible flows on domains with large deformations. United States. https://doi.org/10.1016/j.compfluid.2015.05.026
Wang, Luming, and Persson, Per-Olof. 2015. "A high-order discontinuous Galerkin method with unstructured space–time meshes for two-dimensional compressible flows on domains with large deformations". United States. https://doi.org/10.1016/j.compfluid.2015.05.026. https://www.osti.gov/servlets/purl/1524036.
@article{osti_1524036,
title = {A high-order discontinuous Galerkin method with unstructured space–time meshes for two-dimensional compressible flows on domains with large deformations},
author = {Wang, Luming and Persson, Per-Olof},
abstractNote = {We introduce a high-order accurate space-time discontinuous Galerkin method for solving two-dimensional compressible flow problems on fully unstructured space-time meshes. The discretization is based on a nodal formulation, with appropriate numerical fluxes for the first and the second-order terms, respectively. The scheme is implicit, and we solve the resulting non-linear systems using a parallel Newton-Krylov solver. The meshes are produced by a mesh moving technique with element connectivity updates, and the corresponding space-time elements are produced directly based on these local operations. To obtain globally conforming tetrahedral meshes, we first derive the required conditions on a prism boundary mesh to allow for a valid local triangulation. Next, we present an efficient algorithm for finding a global mesh that satisfies these conditions. We additionally show how to add and remove mesh nodes, again using local constructs for the space-time mesh. Our approach is demonstrated on a number of test problems, showing the high-order accuracy for model problems, and the ability to solve flow problems on domains with complex large deformations.},
doi = {10.1016/j.compfluid.2015.05.026},
url = {https://www.osti.gov/biblio/1524036}, journal = {Computers and Fluids},
issn = {0045-7930},
number = C,
volume = 118,
place = {United States},
year = {Thu Jun 04 00:00:00 EDT 2015},
month = {Thu Jun 04 00:00:00 EDT 2015}
}

Journal Article:

Citation Metrics:
Cited by: 26 works
Citation information provided by
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Figures / Tables:

Figure 1 Figure 1: Space-Time Mesh Generation. The left figure illustrates two mesh layers at time $$t$$ and $$t$$ + $∆t$, and the right figure shows a corresponding 3D space-time mesh between the two layers. The blue faces show a cross-section of the tetrahedral mesh.

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Works referencing / citing this record:

A locally conservative and energy-stable finite-element method for the Navier-Stokes problem on time-dependent domains: HDG for Navier-Stokes on time-dependent domains
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Weight‐adaptive isogeometric analysis for solving elastodynamic problems based on space‐time discretization approach
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Simplex space‐time meshes in compressible flow simulations
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