arXiv subjects

Jacques Peter

Publications and source records attributed to Jacques Peter.

5 recordsLinked to original sources

arXiv2025

ONERA's CRM WBPN database for machine learning activities, related regression challenge and first results

This paper presents a new Computational Fluid Dynamics database, developed at ONERA, to support the advancement of machine learning techniques for aerodynamic field prediction. It contains 468 Reynolds-Averaged Navier-Stokes simulations using the Spalart-Allmaras turbulence model, performed on the NASA/Boeing Common Research Model wing-body-pylon-nacelle configuration. The database spans a wide range of flow conditions, varying Mach number (including transonic regimes), angle of attack (capturing flow separation), and Reynolds number (based on three stagnation pressures, with one setting matching wind tunnel experiments). The quality of the database is assessed, through checking the convergence level of each computation. Based on these data, a regression challenge is defined. It consists in predicting the wall distributions of pressure and friction coefficients for unseen aerodynamic conditions. The 468 simulations are split into training and testing sets, with the training data made available publicly on the Codabench platform. The paper further evaluates several classical machine learning regressors on this task. Tested pointwise methods include Multi-Layer Perceptrons, $\lambda$-DNNs, and Decision Trees, while global methods include Multi-Layer Perceptron, k-Nearest Neighbors, Proper Orthogonal Decomposition and IsoMap. Initial performance results, using $R^2$ scores and worst relative mean absolute error metrics, are presented, offering insights into the capabilities of these techniques for the challenge and references for future work.

cs.LG↗

arXiv2023

Adjoint and direct characteristic equations for two-dimensional compressible Euler flows

The method of characteristics is a classical method for gaining understanding in the solution of a partial differential equation. It has recently been applied to the adjoint equations of the 2D Euler equations and the first goal of this paper is to present a linear algebra analysis that greatly simplifies the discussion of the number of independant characteristic equations satisfied along a family of characteristic curves. This method may be applied for both the direct and the adjoint problem and our second goal is to directly derive in conservative variables the characteristic equations of 2D compressible inviscid flows. Finally, the theoretical results are assessed for a nozzle flow with a classical scheme and its dual consistent discrete adjoint.

physics.flu-dyn↗

arXiv2022

Ordinary differential equations for the adjoint Euler equations

Ordinary Differential Equations are derived for the adjoint Euler equations firstly using the method of characteristics in 2D. For this system of partial-differential equations, the characteristic curves appear to be the streamtraces and the well-known C+ and C- curves of the theory applied to the flow. The differential equations satisfied along the streamtraces in 2D are then extended and demonstrated in 3D by linear combinations of the original adjoint equations. These findings extend their well-known counterparts for the direct system, and should serve analytical and possibly numerical studies of the perfect-flow model with respect to adjoint fields or sensitivity questions. Beside the analytical theory, the results are demonstrated by the numerical integration of the compatibility relationships for discrete 2D flow-fields and dual-consistent adjoint fields over a very fine grid about an airfoil.

math.NA↗

arXiv2020

Analysis of finite-volume discrete adjoint fields for two-dimensional compressible Euler flows

This work deals with a number of questions relative to the discrete and continuous adjoint fields associated with the compressible Euler equations and classical aerodynamic functions. The consistency of the discrete adjoint equations with the corresponding continuous adjoint partial differential equation is one of them. It is has been established or at least discussed only for a handful of numerical schemes and a contribution of this article is to give the adjoint consistency conditions for the 2D Jameson-Schmidt-Turkel scheme in cell-centred finite-volume formulation. The consistency issue is also studied here from a new heuristic point of view by discretizing the continuous adjoint equation for the discrete flow and adjoint fields. Both points of view prove to provide useful information. Besides, it has been often noted that discrete or continuous inviscid lift and drag adjoint exhibit numerical divergence close to the wall and stagnation streamline for a wide range of subsonic and transonic flow conditions. This is analyzed here using the physical source term perturbation method introduced in reference [Giles and Pierce, AIAA Paper 97-1850, 1997]. With this point of view, the fourth physical source term of appears to be the only one responsible for this behavior. It is also demonstrated that the numerical divergence of the adjoint variables corresponds to the response of the flow to the convected increment of stagnation pressure and diminution of entropy created at the source and the resulting change in lift and drag.

physics.comp-ph↗

arXiv2015

Sparse polynomial surrogates for aerodynamic computations with random inputs

This paper deals with some of the methodologies used to construct polynomial surrogate models based on generalized polynomial chaos (gPC) expansions for applications to uncertainty quantification (UQ) in aerodynamic computations. A core ingredient in gPC expansions is the choice of a dedicated sampling strategy, so as to define the most significant scenarios to be considered for the construction of such metamodels. A desirable feature of the proposed rules shall be their ability to handle several random inputs simultaneously. Methods to identify the relative "importance" of those variables or uncertain data shall be ideally considered as well. The present work is more particularly dedicated to the development of sampling strategies based on sparsity principles. Sparse multi-dimensional cubature rules based on general one-dimensional Gauss-Jacobi-type quadratures are first addressed. These sets are non nested, but they are well adapted to the probability density functions with compact support for the random inputs considered in this study. On the other hand, observing that the aerodynamic quantities of interest (outputs) depend only weakly on the cross-interactions between the variable inputs, it is argued that only low-order polynomials shall significantly contribute to their surrogates. This "sparsity-of-effects" trend prompts the use of reconstruction techniques benefiting from the sparsity of the outputs, such as compressed sensing (CS). CS relies on the observation that one only needs a number of samples proportional to the compressed size of the outputs, rather than their uncompressed size, to construct reliable surrogate models. The results obtained with the test case considered in this work corroborate this expected feature.

physics.flu-dyn↗