Effective Boundary Conditions for Laminar Flows over Periodic Rough Boundaries

Effective boundary conditions or wall laws are proposed for a laminar flow over a rough wall with periodic roughness elements. These effective conditions are posed on a regularized boundary which allows the details of the wall to be avoided and dramatically reduces the 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 bidimensional cases.