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Title: A multiscale control volume finite element method for advection–diffusion equations

Abstract

Summary We present a new stabilized method for advection–diffusion equations, which combines a control volume FEM formulation of the governing equations with a novel multiscale approximation of the total flux. The latter incorporates information about the exact solution that cannot be represented on the mesh. To define this flux, we solve the governing equations along suitable mesh segments under the assumption that the flux varies linearly along these segments. This procedure yields second‐order accurate fluxes on the edges of the mesh. Then, we use curl‐conforming elements of the same order to lift these edge fluxes into the mesh elements. In so doing, we obtain a stabilized control volume FEM formulation that is second‐order accurate and does not require mesh‐dependent stabilization parameters. Numerical convergence studies on uniform and nonuniform grids along with several standard advection tests illustrate the computational properties of the new method. Published 2015. This article is a U.S. Government work and is in the public domain in the USA.

Authors:
 [1];  [1];  [1]
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  1. Computational Mathematics Department Sandia National Laboratories Mail Stop 1320, Albuquerque NM 87185‐1320 USA
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1400894
Resource Type:
Publisher's Accepted Manuscript
Journal Name:
International Journal for Numerical Methods in Fluids
Additional Journal Information:
Journal Name: International Journal for Numerical Methods in Fluids Journal Volume: 77 Journal Issue: 11; Journal ID: ISSN 0271-2091
Publisher:
Wiley Blackwell (John Wiley & Sons)
Country of Publication:
United Kingdom
Language:
English

Citation Formats

Bochev, Pavel, Peterson, Kara, and Perego, Mauro. A multiscale control volume finite element method for advection–diffusion equations. United Kingdom: N. p., 2015. Web. doi:10.1002/fld.3998.
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Bochev, Pavel, Peterson, Kara, & Perego, Mauro. A multiscale control volume finite element method for advection–diffusion equations. United Kingdom. https://doi.org/10.1002/fld.3998
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Bochev, Pavel, Peterson, Kara, and Perego, Mauro. Thu . "A multiscale control volume finite element method for advection–diffusion equations". United Kingdom. https://doi.org/10.1002/fld.3998.
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@article{osti_1400894,
title = {A multiscale control volume finite element method for advection–diffusion equations},
author = {Bochev, Pavel and Peterson, Kara and Perego, Mauro},
abstractNote = {Summary We present a new stabilized method for advection–diffusion equations, which combines a control volume FEM formulation of the governing equations with a novel multiscale approximation of the total flux. The latter incorporates information about the exact solution that cannot be represented on the mesh. To define this flux, we solve the governing equations along suitable mesh segments under the assumption that the flux varies linearly along these segments. This procedure yields second‐order accurate fluxes on the edges of the mesh. Then, we use curl‐conforming elements of the same order to lift these edge fluxes into the mesh elements. In so doing, we obtain a stabilized control volume FEM formulation that is second‐order accurate and does not require mesh‐dependent stabilization parameters. Numerical convergence studies on uniform and nonuniform grids along with several standard advection tests illustrate the computational properties of the new method. Published 2015. This article is a U.S. Government work and is in the public domain in the USA.},
doi = {10.1002/fld.3998},
journal = {International Journal for Numerical Methods in Fluids},
number = 11,
volume = 77,
place = {United Kingdom},
year = {Thu Jan 29 00:00:00 EST 2015},
month = {Thu Jan 29 00:00:00 EST 2015}
}
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https://doi.org/10.1002/fld.3998
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