Abstract
In this article we investigate the fluid flow through a thin fracture modelled as a fluid-saturated porous medium. We assume that the fracture has constrictions and that the flow is governed by the prescribed pressure drop between the edges of the fracture. The problem is described by the Darcy-Lapwood-Brinkman model acknowledging the Brinkman extension of the Darcy law as well as the flow inertia. Using asymptotic analysis with respect to the thickness of the fracture, we derive the explicit higher-order approximation for the velocity distribution. We make an error analysis to comment on the order of accuracy of the method used and also to provide rigorous justification for the model.
Acknowledgments
The first author has been supported by the Croatian Science Foundation (project 3955: Mathematical modeling and numerical simulations of processes in thin or porous domains). The second author acknowledges the support for his research under the DST PURSE programme under implementation in the Bangalore University. The authors would like to thank the referees for their helpful comments and suggestions that helped to improve the article.
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