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Shape minimization of the dissipated energy in dyadic trees. (English) Zbl 1232.49027

The goal of this work is to determine the shape of dyadic trees that would minimize the viscous energy of a Newtonian fluid under a volume constraint on the tree. The authors show that for both – low-flow regime and nonlinear flow regime – the optimal structure depends on the fluid boundary conditions that are applied at tree root and leaves. Moreover, the numerical simulations in the nonlinear case give precisely the geometry of the bifurcation.

MSC:

49K30 Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
35Q30 Navier-Stokes equations
65K10 Numerical optimization and variational techniques
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