Reduced Basis Model Order Reduction for Navier-Stokes equations in domains with walls of varying curvature

Abstract

We consider the Navier-Stokes equations in a channel with a narrowing and walls of varying curvature. By applying the empirical interpolation method to generate an affine parameter dependency, the offline-online procedure can be used to compute reduced order solutions for parameter variations. The reduced order space is computed from the steady-state snapshot solutions by a standard POD procedure. The model is discretised with high-order spectral element ansatz functions, resulting in 4752 degrees of freedom. The proposed reduced order model produces accurate approximations of steady-state solutions for a wide range of geometries and kinematic viscosity values. 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 valve shape. Through our computational study, we found that the critical Reynolds number for the symmetry breaking increases as the wall curvature increases.

arXiv commentarXiv admin note: text overlap with arXiv:1812.11051

References in corpus (3)

• A Localized Reduced-Order Modeling Approach for PDEs with Bifurcating Solutions
• Computational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: applications to Coanda effect in cardiology
• On the Application of Reduced Basis Methods to Bifurcation Problems in Incompressible Fluid Dynamics

Cited by in corpus (4)

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• Geometrically Parametrised Reduced Order Models for the Study of Hysteresis of the Coanda Effect in Finite Element-based Incompressible Fluid Dynamics