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Volume 12, Issue 3
Flow and Transport When Scales Are Not Separated: Numerical Analysis and Simulations of Micro- and Macro-Models

Małgorzata Peszyńska, Ralph E. Showalter & Son-Young Yi

Int. J. Numer. Anal. Mod., 12 (2015), pp. 476-515.

Published online: 2015-12

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  • Abstract

In this paper, we consider an upscaled model describing the multiscale flow of a single-phase incompressible fluid and transport of a dissolved chemical by advection and diffusion through a heterogeneous porous medium. Unlike traditional homogenization or volume averaging techniques, we do not assume a good separation of scales. The new model includes as special cases both the classical homogenized model and the double porosity model, but it is characterized by the presence of additional memory terms which describe the effects of local advective transport as well as diffusion. We study the mathematical properties of the memory (convolution) kernels presented in the model and perform rigorous stability analysis of the numerical method to discretize the upscaled model. Some numerical results will be presented to validate the upscaled model and to show the quantitative significance of each memory term in different regimes of flow and transport.

  • Keywords

Upscaled model, double-porosity, memory terms, solute transport, non-separated scale, stability.

  • AMS Subject Headings

35B27, 35R09, 75S05, 74Q15, 65M12, 65M06

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-12-476, author = {Małgorzata Peszyńska, Ralph E. Showalter and Son-Young Yi}, title = {Flow and Transport When Scales Are Not Separated: Numerical Analysis and Simulations of Micro- and Macro-Models}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2015}, volume = {12}, number = {3}, pages = {476--515}, abstract = {

In this paper, we consider an upscaled model describing the multiscale flow of a single-phase incompressible fluid and transport of a dissolved chemical by advection and diffusion through a heterogeneous porous medium. Unlike traditional homogenization or volume averaging techniques, we do not assume a good separation of scales. The new model includes as special cases both the classical homogenized model and the double porosity model, but it is characterized by the presence of additional memory terms which describe the effects of local advective transport as well as diffusion. We study the mathematical properties of the memory (convolution) kernels presented in the model and perform rigorous stability analysis of the numerical method to discretize the upscaled model. Some numerical results will be presented to validate the upscaled model and to show the quantitative significance of each memory term in different regimes of flow and transport.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/499.html} }
TY - JOUR T1 - Flow and Transport When Scales Are Not Separated: Numerical Analysis and Simulations of Micro- and Macro-Models AU - Małgorzata Peszyńska, Ralph E. Showalter & Son-Young Yi JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 476 EP - 515 PY - 2015 DA - 2015/12 SN - 12 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/499.html KW - Upscaled model, double-porosity, memory terms, solute transport, non-separated scale, stability. AB -

In this paper, we consider an upscaled model describing the multiscale flow of a single-phase incompressible fluid and transport of a dissolved chemical by advection and diffusion through a heterogeneous porous medium. Unlike traditional homogenization or volume averaging techniques, we do not assume a good separation of scales. The new model includes as special cases both the classical homogenized model and the double porosity model, but it is characterized by the presence of additional memory terms which describe the effects of local advective transport as well as diffusion. We study the mathematical properties of the memory (convolution) kernels presented in the model and perform rigorous stability analysis of the numerical method to discretize the upscaled model. Some numerical results will be presented to validate the upscaled model and to show the quantitative significance of each memory term in different regimes of flow and transport.

Małgorzata Peszyńska, Ralph E. Showalter and Son-Young Yi. (2015). Flow and Transport When Scales Are Not Separated: Numerical Analysis and Simulations of Micro- and Macro-Models. International Journal of Numerical Analysis and Modeling. 12 (3). 476-515. doi:
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