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We focus on reducing the computational costs associated with the hydrodynamicstability of solutions of the incompressible Navier-Stokes equations for aNewtonian and viscous fluid in contraction-expansion channels. In particular,we are interested in studying steady bifurcations, occurring when non-uniquestable solutions appear as physical and/or geometric control parameters arevaried. The formulation of the stability problem requires solving an eigenvalueproblem for a partial differential operator. An alternative to this approach isthe direct simulation of the flow to characterize the asymptotic behavior ofthe solution. Both approaches can be extremely expensive in terms ofcomputational time. We propose to apply Reduced Order Modeling (ROM) techniquesto reduce the demanding computational costs associated with the detection of atype of steady bifurcations in fluid dynamics. The application that motivatedthe present study is the onset of asymmetries (i.e., symmetry breakingbifurcation) in blood flow through a regurgitant mitral valve, depending on theReynolds number and the regurgitant mitral valve orifice shape.

journal of computational physics

Computational reduction strategies for the detection of steady  bifurcations in incompressible fluid-dynamics: applications to Coanda effect  in cardiology