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Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model

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  • Viviane Klein
  • Malgorzata Peszynska

Abstract

Double-diffusion model is used to simulate slightly compressible fluid flow in periodic porous media as a macro-model in place of the original highly heterogeneous micro-model. In this paper, we formulate an adaptive two-grid numerical finite element discretization of the double-diffusion system and perform a comparison between the micro- and macro-model. Our numerical results show that the micro-model solutions appear to converge to the macro-model linearly with the parameter ε of periodic geometry. For the two-grid discretization, the a priori and a posteriori error estimates are proved, and we show how to adapt the grid for each component independently.

Suggested Citation

  • Viviane Klein & Malgorzata Peszynska, 2012. "Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-26, August.
    • Handle: RePEc:hin:jnljam:938727
    DOI: 10.1155/2012/938727
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