engleski

On the Darcy-Brinkman flow through a channel with slightly perturbed boundary

The goal of this paper is to study the effects of a slightly perturbed boundary on the Darcy- Brinkman flow through a porous channel. We start from a rectangular domain and then perturb the upper part of its boundary by the product of the small parameter $\varepsilon$ and arbitrary smooth function h. Using asymptotic analysis with respect to $\varepsilon$, the effective model has been formally derived. Being in the form of the explicit formulae for the velocity and pressure, the asymptotic approximation clearly shows the nonlocal effects of the small boundary perturbation. The error analysis is also conducted providing the order of accuracy of the asymptotic solution.

boundary perturbation ; Darcy-Brinkman equation ; asymptotic approximation ; error estimates

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