Efficient stability analysis of fluid flows using complex mapping techniques

Abstract

Global linear stability analysis of open flows leads to difficulties associated to boundaiy conditions, leading to either spurious wave reflections (in compressible cases) or to non-local feedback due to the elliptic nature of the pressure equation (in incompressible cases). A nove( approach is introduced to address both these problems. The approach consists of solving the problem using a complex mapping of the spatial coordinates, in a way that can be directly applicable in an existing code without any additional auxiliaiy variable. The efficiency of the method is first demonstrated for a simple 1D equation modeling incompressible Navier-Stokes, and for a linear acoustics problem. The application to full linearized Navier-Stokes equation is then discussed. A criterion on how to select the parameters of the mapping function is derived by analyzing the effect of the mapping on plane wave solutions. Finally, the method is demonstrated for three application cases, including an incompressible jet, a compressible hole-tone configuration and the flow past an airfoil. The examples allow to show that the method allows to suppress the artificial modes which otherwise dominate the spectrum and can possibly hide the physical modes. Finally, it is shown that the method is still efficient for small truncated domains, even in cases where the computational domain is comparable to the dominant wavelength.* The rev iew of Chis paper was arranged by Prof. N.S. Scocc.

Unveiling the competitive role of global modes in the pattern formation of rotating sphere flows

“…Results presented herein follow the same numerical approach adopted by Fabre et al. (2018), Sierra, Fabre & Citro (2020 a ) and Sierra et al. (2020 b ).…”

“…Results presented herein follow the same numerical approach adopted by Fabre et al (2018), Sierra, Fabre & Citro (2020a and Sierra et al (2020b). The calculation of the base flow, the eigenvalue problem and the normal form expansion are implemented in the open-source software FreeFem++.…”

Acoustic instability prediction of the flow through a circular aperture in a thick plate via an impedance criterion

“…The absorbing layer corresponds to the complex mapping technique, cf. Sierra et al (2020). The boundary conditions of the linearized full compressible formulation for the open/open case are as follows:…”

“…Recently, Fabre et al (2019) used the linearized Navier-Stokes equations (LNSE) approach to investigate the unsteady flow through a circular aperture in a thin plate subjected to harmonic forcing. A novel non-reflecting boundary condition called the complex mapping method (Sierra, Fabre & Citro 2020) was introduced to overcome the numerical difficulties created by the strong spatial amplification of the fluctuations. The approach allows computing in a rigorous way the impedance of the hole, namely the ratio between unsteady pressure difference across the orifice and unsteady volume flow rate through the orifice, a quantity which can be directly introduced in more elaborate acoustical models.…”

Etude théorique de l'effet d’un faible courant sur les interactions houle/membrane flexible : application à la récupération d’énergie

“…Afin d'évacuer les ondes loin du domaine une méthode de type ComplexMapping(SIERRA et al, 2019) est de plus mise en oeuvre aux frontières du domaine de calcul. Le principe de cette méthode est d'amortir les ondes afin d'éviter leurs réflexions.…”