Journal of Theoretical
and Applied Mechanics

42, 1, pp. 21-39, Warsaw 2004

Computations of an unsteady viscous flow in a three dimensional system of ducts. Part I: Formulation of the mathematical problem and numerical method

Jacek Szumbarski, Piotr Olszewski, Andrzej Styczek, Jacek Rokicki
Numerical modeling of an unsteady flow of a viscous incompressible fluid inside a branched pipe system is considered. The mathematical formulation is given with special emphasis on inlet/outlet conditions. The equivalent weak form of the initial-boundary value problem is presented. The numerical method based on solutions to particular Stokes problems is proposed and described in some details. Finally, some general remarks about the implementation issues within the framework of the spectral element discretization are made.
Keywords: Navier-Stokes equations; defective boundary conditions; spectral element method