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Volume 24, Issue 5
A Monotone Finite Volume Scheme with Second Order Accuracy for Convection-Diffusion Equations on Deformed Meshes.

Bin Lan, Zhiqiang Sheng & Guangwei Yuan

DOI: 10.4208/cicp.OA-2017-0127

Commun. Comput. Phys., 24 (2018), pp. 1455-1476.

Published online: 2018-06

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  • Abstract

In this paper, we present a new monotone finite volume scheme for the steady state convection-diffusion equation. The discretization of diffusive flux [33] is utilised and a new corrected upwind scheme with second order accuracy for the discretization of convective flux is proposed based on some available informations of diffusive flux. The scheme is locally conservative and monotone on deformed meshes, and has only cell-centered unknowns. Numerical results are presented to show that the scheme obtains second-order accuracy for the solution and first-order accuracy for the flux.

  • Keywords

Convection-diffusion equation, nonlinear, monotone, deformed meshes.

  • AMS Subject Headings

35J15, 35J25, 65M08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-24-1455, author = {Bin Lan, Zhiqiang Sheng and Guangwei Yuan}, title = {A Monotone Finite Volume Scheme with Second Order Accuracy for Convection-Diffusion Equations on Deformed Meshes.}, journal = {Communications in Computational Physics}, year = {2018}, volume = {24}, number = {5}, pages = {1455--1476}, abstract = {

In this paper, we present a new monotone finite volume scheme for the steady state convection-diffusion equation. The discretization of diffusive flux [33] is utilised and a new corrected upwind scheme with second order accuracy for the discretization of convective flux is proposed based on some available informations of diffusive flux. The scheme is locally conservative and monotone on deformed meshes, and has only cell-centered unknowns. Numerical results are presented to show that the scheme obtains second-order accuracy for the solution and first-order accuracy for the flux.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0127}, url = {http://global-sci.org/intro/article_detail/cicp/12485.html} }
TY - JOUR T1 - A Monotone Finite Volume Scheme with Second Order Accuracy for Convection-Diffusion Equations on Deformed Meshes. AU - Bin Lan, Zhiqiang Sheng & Guangwei Yuan JO - Communications in Computational Physics VL - 5 SP - 1455 EP - 1476 PY - 2018 DA - 2018/06 SN - 24 DO - http://doi.org/10.4208/cicp.OA-2017-0127 UR - https://global-sci.org/intro/article_detail/cicp/12485.html KW - Convection-diffusion equation, nonlinear, monotone, deformed meshes. AB -

In this paper, we present a new monotone finite volume scheme for the steady state convection-diffusion equation. The discretization of diffusive flux [33] is utilised and a new corrected upwind scheme with second order accuracy for the discretization of convective flux is proposed based on some available informations of diffusive flux. The scheme is locally conservative and monotone on deformed meshes, and has only cell-centered unknowns. Numerical results are presented to show that the scheme obtains second-order accuracy for the solution and first-order accuracy for the flux.

Bin Lan, Zhiqiang Sheng and Guangwei Yuan. (2018). A Monotone Finite Volume Scheme with Second Order Accuracy for Convection-Diffusion Equations on Deformed Meshes.. Communications in Computational Physics. 24 (5). 1455-1476. doi:10.4208/cicp.OA-2017-0127
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