Abstract

The method of asymptotic partial decomposition of a domain proposed and justified earlier for thin domains (rod structures, tube structures consisting of a set of thin cylinders) generates some special interface conditions between the three-dimensional and one-dimensional parts. In the case of fluid mechanics these conditions prescribe a precomputed Poiseuille-type shape of a solution at the interface, which, however, are not generalizable to the case with a boundary layer in time. In this work we present a new more general version of the method which considered and justified the transient Navier-Stokes equations. Although theoretical justification (well posedness, asymptotic analysis) can be shown only for moderate Reynolds numbers, the provided numerical tests show good accuracies for higher values.