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Effective boundary conditions for laminar flows over periodic rough boundaries. (English) Zbl 0917.76013
Summary: We propose effective boundary conditions or wall laws for a laminar flow over a rough wall with periodic roughness elements. These effective conditions are posed on a regularized boundary which allows to avoid the details of the wall and dramatically reduces computational cost. The effective conditions stem from an asymptotic expansion of the solution, which is presented here. Both first- and second-order conditions are discussed and tested numerically on two-dimensional cases. \(\copyright\) Academic Press.

MSC:
76D05 Navier-Stokes equations for incompressible viscous fluids
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
76M10 Finite element methods applied to problems in fluid mechanics
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