02413nas a2200205   4500008004100000245015800041210006900199260001200268300000800280490000800288520159500296653004301891653002501934653002301959653003401982100002102016700002102037700002102058856012802079       2017                        eng d00aComputational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: Applications to Coanda effect in cardiology0 aComputational reduction strategies for the detection of steady b  c09/2017  a5570 v3443 a<div class="abstract svAbstract " style="border: 0px; font-size: 16px; margin: 0px; padding: 0px; vertical-align: baseline; font-family: Arial, Helvetica, 'Lucida Sans Unicode', 'Microsoft Sans Serif', 'Segoe UI Symbol', STIXGeneral, 'Cambria Math', 'Arial Unicode MS', sans-serif; color: #2e2e2e;" data-etype="ab"><p id="sp0250" style="border: 0px; margin: 0px 0px 9px; padding: 0px; vertical-align: baseline; word-spacing: -0.15ex;">We focus on reducing the computational costs associated with the hydrodynamic stability of solutions of the incompressible Navier–Stokes equations for a Newtonian and viscous fluid in contraction–expansion channels. In particular, we are interested in studying steady bifurcations, occurring when non-unique stable solutions appear as physical and/or geometric control parameters are varied. The formulation of the stability problem requires solving an eigenvalue problem for a partial differential operator. An alternative to this approach is the direct simulation of the flow to characterize the asymptotic behavior of the solution. Both approaches can be extremely expensive in terms of computational time. We propose to apply Reduced Order Modeling (ROM) techniques to reduce the demanding computational costs associated with the detection of a type of steady bifurcations in fluid dynamics. The application that motivated the present study is the onset of asymmetries (i.e., symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the regurgitant mitral valve orifice shape.</p></div>10aParametrized Navier–Stokes equations10aReduced basis method10aStability of flows10aSymmetry breaking bifurcation1 aPitton, Giuseppe1 aQuaini, Annalisa1 aRozza, Gianluigi  uhttps://www.math.sissa.it/publication/computational-reduction-strategies-detection-steady-bifurcations-incompressible-fluid