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Title: A high-order vertex-based central ENO finite-volume scheme for three-dimensional compressible flows

Abstract

High-order discretization methods offer the potential to reduce the computational cost associated with modeling compressible flows. However, it is difficult to obtain accurate high-order discretizations of conservation laws that do not produce spurious oscillations near discontinuities, especially on multi-dimensional unstructured meshes. A novel, high-order, central essentially non-oscillatory (CENO) finite-volume method that does not have these difficulties is proposed for tetrahedral meshes. The proposed unstructured method is vertex-based, which differs from existing cell-based CENO formulations, and uses a hybrid reconstruction procedure that switches between two different solution representations. It applies a high-order k-exact reconstruction in smooth regions and a limited linear reconstruction when discontinuities are encountered. Both reconstructions use a single, central stencil for all variables, making the application of CENO to arbitrary unstructured meshes relatively straightforward. The new approach was applied to the conservation equations governing compressible flows and assessed in terms of accuracy and computational cost. For all problems considered, which included various function reconstructions and idealized flows, CENO demonstrated excellent reliability and robustness. Up to fifth-order accuracy was achieved in smooth regions and essentially non-oscillatory solutions were obtained near discontinuities. The high-order schemes were also more computationally efficient for high-accuracy solutions, i.e., they took less wall time thanmore » the lower-order schemes to achieve a desired level of error. In one particular case, it took a factor of 24 less wall-time to obtain a given level of error with the fourth-order CENO scheme than to obtain the same error with the second-order scheme.« less

Authors:
 [1];  [1];  [1];  [1];  [1]
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  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1214833
Alternate Identifier(s):
OSTI ID: 1254185
Report Number(s):
LA-UR-14-23047
Journal ID: ISSN 0045-7930; PII: S0045793015000651
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Computers and Fluids
Additional Journal Information:
Journal Volume: 114; Journal Issue: C; Journal ID: ISSN 0045-7930
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; numerical algorithms; computational fluid dynamics; high-order methods; compressible flows; shock hydrodynamics

Citation Formats

Charest, Marc R.J., Canfield, Thomas R., Morgan, Nathaniel R., Waltz, Jacob, and Wohlbier, John G. A high-order vertex-based central ENO finite-volume scheme for three-dimensional compressible flows. United States: N. p., 2015. Web. doi:10.1016/j.compfluid.2015.03.001.
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Charest, Marc R.J., Canfield, Thomas R., Morgan, Nathaniel R., Waltz, Jacob, & Wohlbier, John G. A high-order vertex-based central ENO finite-volume scheme for three-dimensional compressible flows. United States. https://doi.org/10.1016/j.compfluid.2015.03.001
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Charest, Marc R.J., Canfield, Thomas R., Morgan, Nathaniel R., Waltz, Jacob, and Wohlbier, John G. Wed . "A high-order vertex-based central ENO finite-volume scheme for three-dimensional compressible flows". United States. https://doi.org/10.1016/j.compfluid.2015.03.001. https://www.osti.gov/servlets/purl/1214833.
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@article{osti_1214833,
title = {A high-order vertex-based central ENO finite-volume scheme for three-dimensional compressible flows},
author = {Charest, Marc R.J. and Canfield, Thomas R. and Morgan, Nathaniel R. and Waltz, Jacob and Wohlbier, John G.},
abstractNote = {High-order discretization methods offer the potential to reduce the computational cost associated with modeling compressible flows. However, it is difficult to obtain accurate high-order discretizations of conservation laws that do not produce spurious oscillations near discontinuities, especially on multi-dimensional unstructured meshes. A novel, high-order, central essentially non-oscillatory (CENO) finite-volume method that does not have these difficulties is proposed for tetrahedral meshes. The proposed unstructured method is vertex-based, which differs from existing cell-based CENO formulations, and uses a hybrid reconstruction procedure that switches between two different solution representations. It applies a high-order k-exact reconstruction in smooth regions and a limited linear reconstruction when discontinuities are encountered. Both reconstructions use a single, central stencil for all variables, making the application of CENO to arbitrary unstructured meshes relatively straightforward. The new approach was applied to the conservation equations governing compressible flows and assessed in terms of accuracy and computational cost. For all problems considered, which included various function reconstructions and idealized flows, CENO demonstrated excellent reliability and robustness. Up to fifth-order accuracy was achieved in smooth regions and essentially non-oscillatory solutions were obtained near discontinuities. The high-order schemes were also more computationally efficient for high-accuracy solutions, i.e., they took less wall time than the lower-order schemes to achieve a desired level of error. In one particular case, it took a factor of 24 less wall-time to obtain a given level of error with the fourth-order CENO scheme than to obtain the same error with the second-order scheme.},
doi = {10.1016/j.compfluid.2015.03.001},
journal = {Computers and Fluids},
number = C,
volume = 114,
place = {United States},
year = {Wed Mar 11 00:00:00 EDT 2015},
month = {Wed Mar 11 00:00:00 EDT 2015}
}
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https://doi.org/10.1016/j.compfluid.2015.03.001
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    Works referencing / citing this record:

    A Novel Multi-Dimensional Limiter for High-Order Finite Volume Methods on Unstructured Grids
    journal, October 2017

    • Liu, Yilang; Zhang, Weiwei; Li, Chunna
    • Communications in Computational Physics, Vol. 22, Issue 5
    • DOI: 10.4208/cicp.oa-2017-0039
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