Backflow stabilization by deconvolution-based large eddy simulation modeling

Abstract

In the numerical simulations of incompressible fluids, the occurrence of incoming flows through outlet boundaries where Neumann conditions are prescribed may introduce the numerical instability known as the backflow instability. This backflow instability is related to the nonlinear convective term and is often challenging the numerical simulation of the blood flow in large vessels. In fact, the alternation of systole and diastole induces backflows at the outlets, which are usually Neumann boundaries since the lack of velocity data requires the prescription of traction/pressure conditions. The Reynolds numbers that trigger the backflow instability are generally moderate (in the range of a few hundreds and above).In this work, we prove that a particular Large Eddy Simulation (LES) model implicitly stabilizes the backflow instability. This LES model uses deconvolution filters and is the basis of the so-called Evolve-Filter-Relax scheme recently introduced by Layton, Rebholz and their collaborators as an effective alternative to Direct Numerical Simulations for the moderate or large Reynolds number flow. With a judicious selection of the parameters of this LES scheme, it is possible to suppress the term that triggers the numerical backflow instability, so to obtain reliable and efficient numerical simulations. This is particularly attractive in computational clinical studies, where many cases need to be studied in a relatively short time.We provide a rigorous proof of our statement and numerical evidence that corroborates the theory on both idealized and realistic cases. For the latter, we consider a patient-specific aortic aneurysm geometry. Aortic simulations feature Reynolds numbers and flow regimes that particularly benefit from this serendipity (aka ‘two-birds-one-stone’) circumstance, where a LES modeling is stabilizing a numerical artifact.