arXiv subjects

Cédric Content

Publications and source records attributed to Cédric Content.

5 recordsLinked to original sources

arXiv2026

Projection method for mean resolvent analysis of periodic flows

The mean resolvent operator predicts the mean linear response to forcing in the frequency domain and provides the optimal linear time-invariant approximation of statistically steady, time-varying flows [1]. We first leverage the harmonic resolvent framework [2,3] in order to propose an algorithm for performing mean resolvent analysis of a periodic flow. Next, we propose an alternative approach which does not explicitly rely on the harmonic resolvent framework. The approach leverages the fact that the mean-flow resolvent approximates the mean resolvent operator; therefore, the optimal forcing modes of the latter operator may be sought in a subspace spanned by optimal modes of the former. This projection approach does not require computing the adjoint dynamics about the attractor, which may be convenient for future extensions to more chaotic and turbulent flows. The present paper is, however, focused on periodic flows, where the convergence of the projection approach can be checked in comparison to the `ground truth' provided by the harmonic resolvent framework. This test is performed on a nearly incompressible axisymmetric laminar jet forced harmonically at the inlet. For the weakly unsteady case, the mean-flow resolvent captures the dominant receptivity peak but misses a secondary one present in the mean resolvent gain. For the strongly unsteady case, the mean-flow resolvent fails to predict the frequency of the vortex-pairing, while the mean resolvent correctly locates the corresponding gain peak. The projection method converges with a subspace dimension of 10 in the weakly unsteady case, while about 100 modes are required for accurate predictions in the strongly unsteady regime. Nonetheless, even a one-dimensional subspace correctly identifies the dominant receptivity peak.

physics.flu-dyn↗

arXiv2026

An End-to-End PyTorch Interface for Differentiable PDE Solvers: A RANS Model-Correction Study

This work presents an end-to-end strategy for solving inverse problems constrained by Partial Differential Equations within a fully differentiable Machine Learning framework. The proposed formulation provides a unified and user-friendly methodology applicable to a wide range of problems, from data assimilation to closure modeling. Our approach combines a baseline differentiable PDE solver, which predicts the state w from the nonlinear system $R(w) = 0$, with a generic additive, parametrized, and differentiable correction $f_ϕ(w)$, with trainable parameters $ϕ$. We show how to optimize phi within a fully differentiable Python workflow by reformulating the PDE as an implicit layer, enabling its integration into arbitrary objective functions, while leveraging PyTorch's automatic differentiation graph. The method is demonstrated on the Reynolds-Averaged Navier-Stokes equations for compressible flows, where the closure term, or a portion of it, is modeled using trainable parameters or a Neural Network. The first application considers the 2D NASA Wall-Mounted Hump test case, where a production-term parameter is optimized against time-averaged LES data. A second application is carried out on the VKI LS-59 turbine blade, where the Spalart-Allmaras eddy viscosity field is reconstructed through the optimization of a trainable spatial field. A dataset is generated starting from the VKI LS-59 turbine blade geometry using the differentiable BROADCAST solver with the Spalart-Allmaras turbulence model. The results highlight the flexibility of the framework, showing its applicability beyond turbulence modeling to a broader class of physics-informed PDE-constrained problems with data-driven components.

cs.CE↗

arXiv2025

Transition mechanisms in hypersonic wind-tunnel nozzles: a methodological approach using global linear stability analysis

Base-flow computations and stability analyses are performed for a hypersonic wind tunnel nozzle at a Mach number of 6. Isothermal and adiabatic wall boundary conditions are investigated, and moderate stagnation conditions are used to provide representative scenarios to study the transition in quiet hypersonic wind tunnel facilities. Under these conditions, the studied nozzle shows a small flow separation at the convergent inlet. Global stability analysis reveals that this recirculation bubble may trigger a classical three-dimensional stationary unstable global mode. Resolvent analysis reveals Görtler, first and second Mack modes affecting the divergent part of the nozzle, along with a Kelvin-Helmholtz instability induced by the bubble. The present study also highlights the key impact of perturbations located in the convergent inlet on the development of instabilities further downstream in the divergent outlet, helping understand the need and efficacy of a suction lip upstream of the nozzle throat to mitigate instabilities in the divergent nozzle. Detailed knowledge of all these mechanisms is essential for understanding flows in quiet hypersonic wind tunnel nozzles and, consequently, represents a key step toward the optimisation of such nozzles.

physics.flu-dyn↗

arXiv2023

Adjoint-based linear sensitivity of a hypersonic boundary layer to steady wall blowing-suction/heating-cooling

For a Mach 4.5 flat-plate adiabatic boundary layer, we study the sensitivity of the first, second Mack modes and streaks to steady wall-normal blowing/suction and wall heat flux. The global instabilities are characterised in frequency space with resolvent gains and their gradients with respect to wall-boundary conditions are derived through a Lagrangian-based method. The implementation is performed in the open-source high-order finite-volume code BROADCAST and Algorithmic Differentiation is used to access the high-order state derivatives of the discretised governing equations. For the second Mack mode, the resolvent optimal gain decreases when suction is applied upstream of Fedorov's mode S/mode F synchronisation point leading to stabilisation and conversely when applied downstream. The largest suction gradient is in the region of branch I of mode S neutral curve. For heat flux control, strong heating at the leading edge stabilises both the first and second Mack modes, the former being more sensitive to wall-temperature control. Streaks are less sensitive to any boundary control in comparison with the Mack modes. Eventually, we show that an optimal actuator consisting of a single steady heating strip located close to the leading edge manages to damp all the instabilities together.

physics.flu-dyn↗

arXiv2023

Global stability analysis of a hypersonic cone-cylinder-flare geometry

Characterizing the boundary layer transition to turbulence around realistic hypersonic vehicles is a challenging task due to the numerous parameters that affect the process. To address this challenge, the cone-cylinder-flare (CCF) geometry has been designed to provide a flow topology that captures various transition mechanisms observed on reentry objects, such as absolute and convective instabilities, which are dependent on the free stream conditions. In this study, a global linear stability analysis is performed on the CCF model at Mach=6.0 to investigate and map the dominant instabilities at wind tunnel flow conditions. We examine optimal responses and forcings computed using resolvent analysis, as well as global modes originating from the recirculation bubble at the cylinder flare junction. The effects of bluntness are assessed through analyses of both blunt and sharp configurations. Our results shed light on the linear flow mechanisms that promote the transition to turbulence around such hypersonic objects.

physics.flu-dyn↗