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In this paper, we present a stabilized mixed formulation for unsteadyBrinkman equation. The formulation is systematically derived based on thevariational multiscale formalism and the method of horizontal lines. Thederivation does not need the assumption that the fine-scale variables do notdepend on the time, which is the case with the conventional derivation ofmultiscale stabilized formulations for transient mixed problems. An expressionfor the stabilization parameter is obtained in terms of a bubble function, andappropriate bubble functions for various finite elements are also presented.Under the proposed formulation, equal-order interpolation for the velocity andpressure (which is computationally the most convenient) is stable.Representative numerical results are presented to illustrate the performance ofthe proposed formulation. Spatial and temporal convergence studies are alsoperformed, and the proposed formulation performed well.

A stabilized mixed formulation for unsteady Brinkman equation based on the method of horizontal lines