A transient analysis of incompressible fluid flow in vessels with moving boundaries

We present in this paper a finite element analysis of Navier‐Stokes equations in a time‐varying domain. The method of weighted residuals is used together with the semi‐discretization approach to obtain the discrete equations. In this approach, where the physical domain is allowed to vary, care is taken to retain the space conservation law property. We describe in detail the transformation of equations between fixed and moving grids. The validity of this method has been tested against two problems which are amenable to analytic solutions. Time accurate results show favorable agreement with analytic solutions. Having verified the applicability of the Galerkin finite element code to problems involving moving grids, we consider the fluid flow in a vessel, where a portion of its boundary moves in time. Results are presented with emphasis on the depiction of vortical flow details.