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Title: A single-stage flux-corrected transport algorithm for high-order finite-volume methods

Abstract

We present a new limiter method for solving the advection equation using a high-order, finite-volume discretization. The limiter is based on the flux-corrected transport algorithm. Here, we modify the classical algorithm by introducing a new computation for solution bounds at smooth extrema, as well as improving the preconstraint on the high-order fluxes. We compute the high-order fluxes via a method-of-lines approach with fourth-order Runge-Kutta as the time integrator. For computing low-order fluxes, we select the corner-transport upwind method due to its improved stability over donor-cell upwind. Several spatial differencing schemes are investigated for the high-order flux computation, including centered- difference and upwind schemes. We show that the upwind schemes perform well on account of the dissipation of high-wavenumber components. The new limiter method retains high-order accuracy for smooth solutions and accurately captures fronts in discontinuous solutions. Further, we need only apply the limiter once per complete time step.

Authors:
 [1];  [1]
+ Show Author Affiliations
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Applied Numerical Algorithms Group, Computational Research Division
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1420104
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Communications in Applied Mathematics and Computational Science
Additional Journal Information:
Journal Volume: 12; Journal Issue: 1; Journal ID: ISSN 1559-3940
Publisher:
Mathematical Sciences Publishers
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; finite-volume method; high order; advection; limiter

Citation Formats

Chaplin, Christopher, and Colella, Phillip. A single-stage flux-corrected transport algorithm for high-order finite-volume methods. United States: N. p., 2017. Web. doi:10.2140/camcos.2017.12.1.
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Chaplin, Christopher, & Colella, Phillip. A single-stage flux-corrected transport algorithm for high-order finite-volume methods. United States. https://doi.org/10.2140/camcos.2017.12.1
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Chaplin, Christopher, and Colella, Phillip. Mon . "A single-stage flux-corrected transport algorithm for high-order finite-volume methods". United States. https://doi.org/10.2140/camcos.2017.12.1. https://www.osti.gov/servlets/purl/1420104.
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@article{osti_1420104,
title = {A single-stage flux-corrected transport algorithm for high-order finite-volume methods},
author = {Chaplin, Christopher and Colella, Phillip},
abstractNote = {We present a new limiter method for solving the advection equation using a high-order, finite-volume discretization. The limiter is based on the flux-corrected transport algorithm. Here, we modify the classical algorithm by introducing a new computation for solution bounds at smooth extrema, as well as improving the preconstraint on the high-order fluxes. We compute the high-order fluxes via a method-of-lines approach with fourth-order Runge-Kutta as the time integrator. For computing low-order fluxes, we select the corner-transport upwind method due to its improved stability over donor-cell upwind. Several spatial differencing schemes are investigated for the high-order flux computation, including centered- difference and upwind schemes. We show that the upwind schemes perform well on account of the dissipation of high-wavenumber components. The new limiter method retains high-order accuracy for smooth solutions and accurately captures fronts in discontinuous solutions. Further, we need only apply the limiter once per complete time step.},
doi = {10.2140/camcos.2017.12.1},
journal = {Communications in Applied Mathematics and Computational Science},
number = 1,
volume = 12,
place = {United States},
year = {Mon May 08 00:00:00 EDT 2017},
month = {Mon May 08 00:00:00 EDT 2017}
}
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https://doi.org/10.2140/camcos.2017.12.1
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