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1999•SIAM Journal on Scientific ComputingRequires access

Mixed Upwinding Covolume Methods on Rectangular Grids for Convection-Diffusion Problems

So‐Hsiang Chou, Do Y. Kwak, Panayot S. Vassilevski

Open publisher page 30 citations

Abstract

We consider an upwinding covolume or control-volume method for a system of first order PDEs resulting from the mixed formulation of a convection-diffusion equation with a variable anisotropic diffusion tensor. The system can be used to model the steady state of the transport of a contaminant carried by a flow. We use the lowest order Raviart--Thomas space and show that the concentration and concentration flux both converge at one-half order provided that the exact flux is in $H^1(\Omega)^2$ and the exact concentration is in $H^1(\Omega)$. Some numerical experiments illustrating the error behavior of the scheme are provided.

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What this paper is about

We consider an upwinding covolume or control-volume method for a system of first order PDEs resulting from the mixed formulation of a convection-diffusion equation with a variable anisotropic diffusion tensor. The system can be used to model the steady state of the transport of a contaminant carried by a flow. We use the lowest order Raviart--Thomas space and show that the concentration and concentration flux both converge at one-half order provided that the exact flux is in $H^1(\Omega)^2$ and the exact concentration is in $H^1(\Omega)$. Some numerical experiments illustrating the error behavior of the scheme are provided.

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Available abstract

We consider an upwinding covolume or control-volume method for a system of first order PDEs resulting from the mixed formulation of a convection-diffusion equation with a variable anisotropic diffusion tensor. The system can be used to model the steady state of the transport of a contaminant carried by a flow. We use the lowest order Raviart--Thomas space and show that the concentration and concentration flux both converge at one-half order provided that the exact flux is in $H^1(\Omega)^2$ and the exact concentration is in $H^1(\Omega)$. Some numerical experiments illustrating the error behavior of the scheme are provided.

Key concepts: Upwind scheme, Mathematics, Convection–diffusion equation, Control volume, Diffusion, Tensor (intrinsic definition), Applied mathematics, Mathematical analysis

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