Abstract
In this study, we justify a modified stationary Navier–Stokes system involving the damping effect for a channel flow with periodic roughness. We solve the modified Navier–Stokes system in a smooth extended channel after reducing the rough boundary to a parameter in a linear damping term. We find that the proposed damping term is valid when the size and amplitude of the imperfection tend to zero. Furthermore, the term yields an O(ε3/2) quadratic approximation of real flow, i.e. O(ε3/2) approximation in the L2-norm, for a small pressure difference. An effective mass flow is also determined up to an order of O(ε3/2).
Original language | English |
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Pages (from-to) | 902-918 |
Number of pages | 17 |
Journal | Applicable Analysis |
Volume | 97 |
Issue number | 6 |
DOIs | |
State | Published - 26 Apr 2018 |
Keywords
- Damping effect
- Navier–Stokes equations
- rough boundary