  Simulating the interaction of fluids with immersed moving solids is playing
an important role for gaining a better quantitative understanding of how fluid
dynamics is altered by the presence of obstacles and which forces are exerted
on the solids by the moving fluid. Such problems appear in various contexts,
ranging from numerous technical applications such as turbines to medical
problems such as the regulation of hemodyamics by valves. Typically, the
numerical treatment of such problems is posed within a fluid structure
interaction (FSI) framework. General FSI models are able to capture
bidirectional interactions, but are challenging to solve and computationally
expensive. Simplified methods offer a possible remedy by achieving better
computational efficiency to broaden the scope to demanding application problems
with focus on understanding the effect of solids on altering fluid dynamics. In
this study we report on the development of a novel method for such
applications. In our method rigid moving obstacles are incorporated in a fluid
dynamics context using concepts from porous media theory. Based on the
Navier-Stokes-Brinkman equations which augments the Navier-Stokes equation with
a Darcy drag term our method represents solid obstacles as time-varying regions
containing a porous medium of vanishing permeability. Numerical stabilization
and turbulence modeling is dealt with by using a residual based variational
multiscale formulation. The key advantages of our approach -- computational
efficiency and ease of implementation -- are demonstrated by solving a standard
benchmark problem of a rotating blood pump posed by the Food and Drug
Administration Agency (FDA). Validity is demonstrated by conducting a mesh
convergence study and by comparison against the extensive set of experimental
data provided for this benchmark.

Fluid Dynamics