Premium
A stabilized mixed formulation for unsteady Brinkman equation based on the method of horizontal lines
Author(s) -
Srinivasan Shriram,
Nakshatrala K. B.
Publication year - 2011
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2544
Subject(s) - interpolation (computer graphics) , formalism (music) , mathematics , bubble , convergence (economics) , mathematical analysis , mechanics , classical mechanics , physics , motion (physics) , art , musical , economics , visual arts , economic growth
In this paper, we present a stabilized mixed formulation for unsteady Brinkman equation. The formulation is systematically derived based on the variational multiscale formalism and the method of horizontal lines. The derivation does not need the assumption that the fine‐scale variables do not depend on the time, which is the case with the conventional derivation of multiscale stabilized formulations for transient mixed problems. An expression for the stabilization parameter is obtained in terms of a bubble function, and appropriate bubble functions for various finite elements are also presented. Under the proposed formulation, equal‐order interpolation for the velocity and pressure (which is computationally the most convenient) is stable. Representative numerical results are presented to illustrate the performance of the proposed formulation. Spatial and temporal convergence studies are also performed, and the proposed formulation performed well. Copyright © 2011 John Wiley & Sons, Ltd.