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Volume 2, Issue 4
Multiscale Finite Element Modelling of Flow Through Porous Media with Curved and Contracting Boundaries to Evaluate Different Types of Bubble Functions

V. Nassehi, M. Parvazinia & A. Khan

Commun. Comput. Phys., 2 (2007), pp. 723-745.

Published online: 2007-02

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  • Abstract

The Brinkman equation is used to model the isothermal flow of the Newtonian fluids through highly permeable porous media. Due to the multiscale behaviour of this flow regime the standard Galerkin finite element schemes for the Brinkman equation require excessive mesh refinement at least in the vicinity of domain walls to yield stable and accurate results. To avoid this, a multiscale finite element method is developed using bubble functions. It is shown that by using bubble enriched shape functions the standard Galerkin method can generate stable solutions without excessive near wall mesh refinements. In this paper the performances of different types of bubble functions are evaluated. These functions are used in conjunction with bilinear Lagrangian elements to solve the Brinkman equation via a penalty finite element scheme.

  • Keywords

Finite element, multiscale method, porous media, Newtonian fluid flow, bubble function, static condensation.

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COPYRIGHT: © Global Science Press

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@Article{CiCP-2-723, author = {V. Nassehi, M. Parvazinia and A. Khan}, title = {Multiscale Finite Element Modelling of Flow Through Porous Media with Curved and Contracting Boundaries to Evaluate Different Types of Bubble Functions}, journal = {Communications in Computational Physics}, year = {2007}, volume = {2}, number = {4}, pages = {723--745}, abstract = {

The Brinkman equation is used to model the isothermal flow of the Newtonian fluids through highly permeable porous media. Due to the multiscale behaviour of this flow regime the standard Galerkin finite element schemes for the Brinkman equation require excessive mesh refinement at least in the vicinity of domain walls to yield stable and accurate results. To avoid this, a multiscale finite element method is developed using bubble functions. It is shown that by using bubble enriched shape functions the standard Galerkin method can generate stable solutions without excessive near wall mesh refinements. In this paper the performances of different types of bubble functions are evaluated. These functions are used in conjunction with bilinear Lagrangian elements to solve the Brinkman equation via a penalty finite element scheme.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7924.html} }
TY - JOUR T1 - Multiscale Finite Element Modelling of Flow Through Porous Media with Curved and Contracting Boundaries to Evaluate Different Types of Bubble Functions AU - V. Nassehi, M. Parvazinia & A. Khan JO - Communications in Computational Physics VL - 4 SP - 723 EP - 745 PY - 2007 DA - 2007/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7924.html KW - Finite element, multiscale method, porous media, Newtonian fluid flow, bubble function, static condensation. AB -

The Brinkman equation is used to model the isothermal flow of the Newtonian fluids through highly permeable porous media. Due to the multiscale behaviour of this flow regime the standard Galerkin finite element schemes for the Brinkman equation require excessive mesh refinement at least in the vicinity of domain walls to yield stable and accurate results. To avoid this, a multiscale finite element method is developed using bubble functions. It is shown that by using bubble enriched shape functions the standard Galerkin method can generate stable solutions without excessive near wall mesh refinements. In this paper the performances of different types of bubble functions are evaluated. These functions are used in conjunction with bilinear Lagrangian elements to solve the Brinkman equation via a penalty finite element scheme.

V. Nassehi, M. Parvazinia and A. Khan. (2007). Multiscale Finite Element Modelling of Flow Through Porous Media with Curved and Contracting Boundaries to Evaluate Different Types of Bubble Functions. Communications in Computational Physics. 2 (4). 723-745. doi:
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