High-order approximations for an incompressible viscous flow on a rough boundary

Abstract

In this paper, we propose approximations of fluid flow that could be used for obtaining wall laws of higher order. We consider the two-dimensional laminar fluid flow, modeled by the incompressible Stokes system in a straight channel with a rough side. The roughness is periodic and the ratio of the amplitude of the rough part and the size of the flow domain is denoted by ϵ, being a small number. We impose periodic boundary conditions on the flow. We generalize the boundary layers needed for the construction of flow approximations of higher order with respect to ϵ. The existence of the layers and their features are discussed. Finally we give the error estimates for the approximations and establish an explicit wall law.

Keywords:

• Stokes equations
• boundary layers
• rough boundary
• high-order approximations
• error estimates

AMS Subject Classifications:

• 49K20
• 76D03
• 76D07
• 76D10

Notes

This research was supported by the Ministry of Science, Education and Sports, Croatia [grant number 037-0372787-2797].