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Title: A freestream-preserving fourth-order finite-volume method in mapped coordinates with adaptive-mesh refinement

Abstract

We present a fourth-order accurate finite-volume method for solving time-dependent hyperbolic systems of conservation laws on mapped grids that are adaptively refined in space and time. Some novel considerations for formulating the semi-discrete system of equations in computational space are combined with detailed mechanisms for accommodating the adapting grids. Furthermore, these considerations ensure that conservation is maintained and that the divergence of a constant vector field is always zero (freestream-preservation property). The solution in time is advanced with a fourth-order Runge-Kutta method. A series of tests verifies that the expected accuracy is achieved in smooth flows and the solution of a Mach reflection problem demonstrates the effectiveness of the algorithm in resolving strong discontinuities.

Authors:
 [1];  [1];  [1];  [2];  [2]
+ Show Author Affiliations
  1. Colorado State Univ., Fort Collins, CO (United States). Computational Fluid Dynamics and Propulsion Lab.
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Applied Numerical Algorithms Group
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
OSTI Identifier:
1378703
Alternate Identifier(s):
OSTI ID: 1245246
Grant/Contract Number:  
AC02-05CH11231; AC52-07NA27344; EE0006086
Resource Type:
Accepted Manuscript
Journal Name:
Computers and Fluids
Additional Journal Information:
Journal Volume: 123; Journal Issue: C; Journal ID: ISSN 0045-7930
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; High-order finite-volume method; Freestream-preserving; Mapped grids; Adaptive-mesh refinement; Finite-volume method; Hyperbolic conservation laws

Citation Formats

Guzik, Stephen M., Gao, Xinfeng, Owen, Landon D., McCorquodale, Peter, and Colella, Phillip. A freestream-preserving fourth-order finite-volume method in mapped coordinates with adaptive-mesh refinement. United States: N. p., 2015. Web. doi:10.1016/j.compfluid.2015.10.001.
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Guzik, Stephen M., Gao, Xinfeng, Owen, Landon D., McCorquodale, Peter, & Colella, Phillip. A freestream-preserving fourth-order finite-volume method in mapped coordinates with adaptive-mesh refinement. United States. https://doi.org/10.1016/j.compfluid.2015.10.001
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Guzik, Stephen M., Gao, Xinfeng, Owen, Landon D., McCorquodale, Peter, and Colella, Phillip. Sun . "A freestream-preserving fourth-order finite-volume method in mapped coordinates with adaptive-mesh refinement". United States. https://doi.org/10.1016/j.compfluid.2015.10.001. https://www.osti.gov/servlets/purl/1378703.
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@article{osti_1378703,
title = {A freestream-preserving fourth-order finite-volume method in mapped coordinates with adaptive-mesh refinement},
author = {Guzik, Stephen M. and Gao, Xinfeng and Owen, Landon D. and McCorquodale, Peter and Colella, Phillip},
abstractNote = {We present a fourth-order accurate finite-volume method for solving time-dependent hyperbolic systems of conservation laws on mapped grids that are adaptively refined in space and time. Some novel considerations for formulating the semi-discrete system of equations in computational space are combined with detailed mechanisms for accommodating the adapting grids. Furthermore, these considerations ensure that conservation is maintained and that the divergence of a constant vector field is always zero (freestream-preservation property). The solution in time is advanced with a fourth-order Runge-Kutta method. A series of tests verifies that the expected accuracy is achieved in smooth flows and the solution of a Mach reflection problem demonstrates the effectiveness of the algorithm in resolving strong discontinuities.},
doi = {10.1016/j.compfluid.2015.10.001},
journal = {Computers and Fluids},
number = C,
volume = 123,
place = {United States},
year = {Sun Dec 20 00:00:00 EST 2015},
month = {Sun Dec 20 00:00:00 EST 2015}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1016/j.compfluid.2015.10.001
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    Works referencing / citing this record:

    Correction: A Fourth-Order Finite-Volume Method with Adaptive Mesh Refinement for the Multifluid Plasma Model
    conference, January 2018

    • Polak, Scott; Gao, Xinfeng
    • 2018 AIAA Aerospace Sciences Meeting, 2018 AIAA Aerospace Sciences Meeting
    • DOI: 10.2514/6.2018-2195.c1
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