American Institute of Mathematical Sciences

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July  2005, 13(4): 941-960. doi: 10.3934/dcds.2005.13.941

A new upscaling method for the solute transport equations

Zhiming Chen 1, , Weibing Deng 2, and  Huang Ye 1,

1. 

LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China, China
2. 

Department of Mathematics, Nanjing University, Nanjing 210093, China

Received  September 2004 Revised  February 2005 Published  August 2005

This paper proposes a new upscaling method in the simulations of solute transport in heterogeneous media. We provide a detailed convergence analysis of the method under the assumption that the oscillating coefficients are periodic. While such a simplifying assumption is not required by our method, it allows us to use homogenization theory to obtain the asymptotic structure of the solutions. Numerical experiments are carried out for solute transport in a porous medium with a random log-normal relative permeability to demonstrate the efficiency and accuracy of the proposed method.
Keywords: solute transport equation., homogenization, Upscaling.
Mathematics Subject Classification: Primary: 65M60, 65N30; Secondary: 76M1.
Citation: Zhiming Chen, Weibing Deng, Huang Ye. A new upscaling method for the solute transport equations. Discrete & Continuous Dynamical Systems - A, 2005, 13 (4) : 941-960. doi: 10.3934/dcds.2005.13.941
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