Viscous fluid flow in bifurcating channels and pipes [Elektronische Ressource] / vorgelegt von Michael Lenzinger

Inaugural-DissertationzurErlangung der Doktorwu¨rdederNaturwissenschaftlich-Mathematischen Gesamtfakult¨atderRuprecht-Karls-Universit¨atHeidelbergvorgelegt vonMichael Lenzingeraus KonstanzTag der mu¨ndlichen Pru¨fung:18. Januar 2006Viscous Fluid Flowin Bifurcating Channels and PipesGutachter:Prof. Dr. Drs. h.c. Willi J¨agerProf. Dr. Ben SchweizerAbstractIn the present thesis the flow of a viscous Newtonian fluid in a bifurcation of thinthree-dimensional pipes with a diameter-to-length ratio of order O(ǫ) is studied. Themodel is based on the steady-state Navier-Stokes equations with pressure conditions onthe in- and outflow boundaries. Existence and local uniqueness is proven under theassumption of small data represented by a Reynolds number Re of order O(ǫ).ǫOur aim is to construct an asymptotic expansion in powers of ǫ and Re for the solu-ǫtion of this Navier-Stokes problem. In the first part of the thesis we therefore presenta formal method of computing the pressure drop and the flux based on Poiseuille flow.In contrast to the existing literature, we also analyze the influence of the bifurcationgeometry on the fluid flow by introducing local Stokes problems in the junction. Weshow that the solutions of these Stokes problems in the junction of diameterO(M) ap-proximate the solutions of the corresponding Leray problems in the infinite bifurcationup to an error decaying exponentially in M.