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Title: A coupled discontinuous Galerkin-Finite Volume framework for solving gas dynamics over embedded geometries

Abstract

We present a computational framework for solving the equations of inviscid gas dynamics using structured grids with embedded geometries. The novelty of the proposed approach is the use of high-order discontinuous Galerkin (dG) schemes and a shock-capturing Finite Volume (FV) scheme coupled via an hp adaptive mesh refinement (hp-AMR) strategy that offers high-order accurate resolution of the embedded geometries. The hp-AMR strategy is based on a multi-level block-structured domain partition in which each level is represented by block-structured Cartesian grids and the embedded geometry is represented implicitly by a level set function. The intersection of the embedded geometry with the grids produces the implicitly-defined mesh that consists of a collection of regular rectangular cells plus a relatively small number of irregular curved elements in the vicinity of the embedded boundaries. High-order quadrature rules for implicitly-defined domains enable high-order accuracy resolution of the curved elements with a cell-merging strategy to address the small-cell problem. The hp-AMR algorithm treats the system with a second-order finite volume scheme at the finest level to dynamically track the evolution of solution discontinuities while using dG schemes at coarser levels to provide high-order accuracy in smooth regions of the flow. On the dG levels, the methodologymore » supports different orders of basis functions on different levels. The space-discretized governing equations are then advanced explicitly in time using high-order Runge-Kutta algorithms. Numerical tests are presented for two-dimensional and three-dimensional problems involving an ideal gas. The results are compared with both analytical solutions and experimental observations and demonstrate that the framework provides high-order accuracy for smooth flows and accurately captures solution discontinuities.« less

Authors:
ORCiD logo [1];  [1];  [1]
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  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1815406
Alternate Identifier(s):
OSTI ID: 1833882; OSTI ID: 1923891
Grant/Contract Number:  
AC02-05CH11231; AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 450; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Embedded boundaries; Discontinuous Galerkin methods; Finite Volume methods; Shock-capturing schemes; hp-AMR

Citation Formats

Gulizzi, Vincenzo, Almgren, Ann S., and Bell, John B. A coupled discontinuous Galerkin-Finite Volume framework for solving gas dynamics over embedded geometries. United States: N. p., 2021. Web. doi:10.1016/j.jcp.2021.110861.
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Gulizzi, Vincenzo, Almgren, Ann S., & Bell, John B. A coupled discontinuous Galerkin-Finite Volume framework for solving gas dynamics over embedded geometries. United States. https://doi.org/10.1016/j.jcp.2021.110861
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Gulizzi, Vincenzo, Almgren, Ann S., and Bell, John B. Tue . "A coupled discontinuous Galerkin-Finite Volume framework for solving gas dynamics over embedded geometries". United States. https://doi.org/10.1016/j.jcp.2021.110861. https://www.osti.gov/servlets/purl/1815406.
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@article{osti_1815406,
title = {A coupled discontinuous Galerkin-Finite Volume framework for solving gas dynamics over embedded geometries},
author = {Gulizzi, Vincenzo and Almgren, Ann S. and Bell, John B.},
abstractNote = {We present a computational framework for solving the equations of inviscid gas dynamics using structured grids with embedded geometries. The novelty of the proposed approach is the use of high-order discontinuous Galerkin (dG) schemes and a shock-capturing Finite Volume (FV) scheme coupled via an hp adaptive mesh refinement (hp-AMR) strategy that offers high-order accurate resolution of the embedded geometries. The hp-AMR strategy is based on a multi-level block-structured domain partition in which each level is represented by block-structured Cartesian grids and the embedded geometry is represented implicitly by a level set function. The intersection of the embedded geometry with the grids produces the implicitly-defined mesh that consists of a collection of regular rectangular cells plus a relatively small number of irregular curved elements in the vicinity of the embedded boundaries. High-order quadrature rules for implicitly-defined domains enable high-order accuracy resolution of the curved elements with a cell-merging strategy to address the small-cell problem. The hp-AMR algorithm treats the system with a second-order finite volume scheme at the finest level to dynamically track the evolution of solution discontinuities while using dG schemes at coarser levels to provide high-order accuracy in smooth regions of the flow. On the dG levels, the methodology supports different orders of basis functions on different levels. The space-discretized governing equations are then advanced explicitly in time using high-order Runge-Kutta algorithms. Numerical tests are presented for two-dimensional and three-dimensional problems involving an ideal gas. The results are compared with both analytical solutions and experimental observations and demonstrate that the framework provides high-order accuracy for smooth flows and accurately captures solution discontinuities.},
doi = {10.1016/j.jcp.2021.110861},
journal = {Journal of Computational Physics},
number = ,
volume = 450,
place = {United States},
year = {Tue Nov 23 00:00:00 EST 2021},
month = {Tue Nov 23 00:00:00 EST 2021}
}
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