Optimal Bounds on Energy Dissipation for Stress-driven Shear Flows

Abstract eng:
A novel method is proposed to provide bounds on energy dissipation for stress-driven flows. The particular approach is based upon the fact that the background method for establishing bounds on emergent quantities for fluid flows typically requires the solution of an infinite dimensional variational problem. We show how such a problem can be rigorously relaxed so that a feasible solution can be found by instead solving an associated finite-dimensional convex optimization problem. In particular, we make use of Semidefinite-Programming methods, for which established and efficient solution methods are available. We apply this new technique to compute near-optimal upper bounds on the dissipation coefficient for stress-driven shear flows, improving previously known bounds by more than 10 times.

• Export as: BibTeX | MARC | MARCXML | DC | EndNote | NLM | RefWorks
• Add to your basket