Reduced Navier-Stokes equations near a flow boundary

We derive a hierarchy of PDEs for the leading-order evolution of wall-based quantities, such as the-skin-friction and the wall-pressure gradient, in two-dimensional fluid flows. The resulting Reduced Navier-Stokes (RNS) equations are defined on the boundary of the flow, and hence have reduced spatial dimensionality compared to the Navier-Stokes equations. This spatial reduction speeds up numerical computations and makes the equations attractive candidates for flow-control design. We prove that members of the RNS hierarchy are well-posed if appended with boundary-conditions obtained from wall-based sensors. We also derive the lowest-order RNS equations for three-dimensional flows. For several benchmark problems, our numerical simulations show close finite-time agreement between the solutions of RNS and those of the full Navier-Stokes equations. (c) 2006 Elsevier B.V. All rights reserved.


Published in:
Physica D, 217, 2, 161-185
Year:
2006
Publisher:
Elsevier
ISSN:
0167-2789
Keywords:
Laboratories:




 Record created 2013-11-12, last modified 2018-09-13

Publisher's version:
Download fulltext
PDF

Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)