article

A Fourth-Order Accurate Finite-Volume Method with Structured Adaptive Mesh Refinement for Solving the Advection-Diffusion Equation

Authors:

Phillip ColellaAuthors Info & Claims

SIAM Journal on Scientific Computing, Volume 34, Issue 2

Pages 179 - 201

https://doi.org/10.1137/110820105

Published: 01 April 2012 Publication History

Abstract

We present a fourth-order accurate algorithm for solving Poisson's equation, the heat equation, and the advection-diffusion equation on a hierarchy of block-structured, adaptively refined grids. For spatial discretization, finite-volume stencils are derived for the divergence operator and Laplacian operator in the context of structured adaptive mesh refinement and a variety of boundary conditions; the resulting linear system is solved with a multigrid algorithm. For time integration, we couple the elliptic solver to a fourth-order accurate Runge-Kutta method, introduced by Kennedy and Carpenter [Appl. Numer. Math., 44 (2003), pp. 139-181], which enables us to treat the nonstiff advection term explicitly and the stiff diffusion term implicitly. We demonstrate the spatial and temporal accuracy by comparing results with analytical solutions. Because of the general formulation of the approach, the algorithm is easily extensible to more complex physical systems.

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Cited By

Christopher JFalgout RSchroder JGuzik SGao X(2020)A space-time parallel algorithm with adaptive mesh refinement for computational fluid dynamicsComputing and Visualization in Science10.1007/s00791-020-00334-123:1-4Online publication date: 27-Sep-2020
https://dl.acm.org/doi/10.1007/s00791-020-00334-1
Brehm CBarad MKiris C(2019)Development of immersed boundary computational aeroacoustic prediction capabilities for open-rotor noiseJournal of Computational Physics10.1016/j.jcp.2019.02.011388:C(690-716)Online publication date: 1-Jul-2019
https://dl.acm.org/doi/10.1016/j.jcp.2019.02.011
Del Sarto DDeriaz E(2017)A multigrid AMR algorithm for the study of magnetic reconnectionJournal of Computational Physics10.1016/j.jcp.2017.08.046351:C(511-533)Online publication date: 15-Dec-2017
https://dl.acm.org/doi/10.1016/j.jcp.2017.08.046
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A Fourth-Order Accurate Finite-Volume Method with Structured Adaptive Mesh Refinement for Solving the Advection-Diffusion Equation
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations

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cover image SIAM Journal on Scientific Computing

SIAM Journal on Scientific Computing Volume 34, Issue 2

April 2012

829 pages

ISSN:1064-8275

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 April 2012

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Cited By

Christopher JFalgout RSchroder JGuzik SGao X(2020)A space-time parallel algorithm with adaptive mesh refinement for computational fluid dynamicsComputing and Visualization in Science10.1007/s00791-020-00334-123:1-4Online publication date: 27-Sep-2020
https://dl.acm.org/doi/10.1007/s00791-020-00334-1
Brehm CBarad MKiris C(2019)Development of immersed boundary computational aeroacoustic prediction capabilities for open-rotor noiseJournal of Computational Physics10.1016/j.jcp.2019.02.011388:C(690-716)Online publication date: 1-Jul-2019
https://dl.acm.org/doi/10.1016/j.jcp.2019.02.011
Del Sarto DDeriaz E(2017)A multigrid AMR algorithm for the study of magnetic reconnectionJournal of Computational Physics10.1016/j.jcp.2017.08.046351:C(511-533)Online publication date: 15-Dec-2017
https://dl.acm.org/doi/10.1016/j.jcp.2017.08.046
(2017)High-order finite-volume solutions of the steady-state advectiondiffusion equation with nonlinear Robin boundary conditionsJournal of Computational Physics10.1016/j.jcp.2017.05.023345:C(358-372)Online publication date: 15-Sep-2017
https://dl.acm.org/doi/10.1016/j.jcp.2017.05.023
Henderson NPena L(2017)The inverse distance weighted interpolation applied to a particular form of the path tubes MethodApplied Mathematics and Computation10.1016/j.amc.2017.01.053304:C(114-135)Online publication date: 1-Jul-2017
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Zhang Q(2016)GePUPJournal of Scientific Computing10.1007/s10915-015-0122-467:3(1134-1180)Online publication date: 1-Jun-2016
https://dl.acm.org/doi/10.1007/s10915-015-0122-4
Crouseilles NKuhn MLatu G(2015)Comparison of Numerical Solvers for Anisotropic Diffusion Equations Arising in Plasma PhysicsJournal of Scientific Computing10.1007/s10915-015-9999-165:3(1091-1128)Online publication date: 1-Dec-2015
https://dl.acm.org/doi/10.1007/s10915-015-9999-1

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