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

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]
  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:
Grant/Contract Number:
AC02-05CH11231; AC52-07NA27344; EE0006086
Type:
Accepted Manuscript
Journal Name:
Computers and Fluids
Additional Journal Information:
Journal Volume: 123; Journal Issue: C; Journal ID: ISSN 0045-7930
Publisher:
Elsevier
Research Org:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
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
OSTI Identifier:
1378703
Alternate Identifier(s):
OSTI ID: 1245246

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., Web. doi:10.1016/j.compfluid.2015.10.001.
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. doi:10.1016/j.compfluid.2015.10.001.
Guzik, Stephen M., Gao, Xinfeng, Owen, Landon D., McCorquodale, Peter, and Colella, Phillip. 2015. "A freestream-preserving fourth-order finite-volume method in mapped coordinates with adaptive-mesh refinement". United States. doi:10.1016/j.compfluid.2015.10.001. https://www.osti.gov/servlets/purl/1378703.
@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 = {2015},
month = {12}
}