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Different effective boundary conditions or wall laws for unsteady incompressible Navier-Stokes equations over rough domains are derived in the laminar setting. First and second order unsteady wall laws are proposed using two scale asymptotic expansion techniques. The roughness elements are supposed to be periodic and the influence of the rough boundary is incorporated through constitutive constants. These constants are obtained by solving steady Stokes problems and so they are calculated only once....
Different effective boundary conditions or wall laws for unsteady incompressible Navier-Stokes equations over rough
domains are derived in the laminar setting. First and second order unsteady wall laws are proposed using two scale asymptotic
expansion techniques. The roughness elements are supposed to be periodic and the influence of the
rough boundary is incorporated through constitutive constants. These constants are obtained by solving steady
Stokes problems and so they are calculated only...
In this paper we introduce a coupled systems of kinetic equations for
the linearized Carleman model. We then study the existence
theory and
the asymptotic behaviour of the resulting coupled problem. In order to
solve the coupled problem we propose to use the time marching algorithm.
We then develop a convergence theory for the resulting algorithm. Numerical
results confirming the theory are then presented.
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