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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…

Machine Learning · Computer Science 2025-05-13 Jacques Peter , Quentin Bennehard , Sébastien Heib , Jean-Luc Hantrais-Gervois , Frédéric Moëns

In this work we propose, {analyze}, and validate a stabilized finite element method for a flow problem arising from the assessment of {4D Flow Magnetic Resonance Imaging quality}. Starting from the Navier-Stokes equation and splitting its…

Numerical Analysis · Mathematics 2026-01-27 Gabriel Barrenechea , Cristian Cárcamo , Abner Poza

In this paper, we consider up-to-date and classical Finite Element (FE) stabilized methods for time-dependent incompressible flows. All studied methods belong to the Variational MultiScale (VMS) framework. So, different realizations of…

Numerical Analysis · Mathematics 2018-04-10 Naveed Ahmed , Samuele Rubino

We present a generative reduced basis (RB) approach to construct reduced order models for parametrized partial differential equations. Central to this approach is the construction of generative RB spaces that provide rapidly convergent…

Numerical Analysis · Mathematics 2024-10-08 Ngoc Cuong Nguyen

A general method for accelerating fixed point schemes for problems related to partial differential equations is presented in this article. The speedup is obtained by training a reduced-order model on-the-fly, removing the need to do an…

Numerical Analysis · Mathematics 2025-12-01 Philippe-André Luneau , Jean Deteix

Inf-sup stable FEM applied to time-dependent incompressible Navier-Stokes flows are considered. The focus lies on robust estimates for the kinetic and dissipation energies in a twofold sense. Firstly, pressure-robustness ensures the…

Numerical Analysis · Mathematics 2019-04-12 Philipp W. Schroeder , Christoph Lehrenfeld , Alexander Linke , Gert Lube

We consider a class of parameter-dependent optimal control problems of elliptic PDEs with constraints of general type on the control variable. Applying the concept of variational discretization, [4], together with techniques from the…

Optimization and Control · Mathematics 2018-08-20 Ahmad Ahmad Ali , Michael Hinze

In this paper we establish a stability barrier of a class of high-order Hermite-type discretization of 1D advection equations underlying the hybrid-variable (HV) and active flux (AF) methods. These methods seek numerical approximations to…

Numerical Analysis · Mathematics 2025-05-12 Xianyi Zeng

In this paper, a new localized radial basis function (RBF) method based on partition of unity (PU) is proposed for solving boundary and initial-boundary value problems. The new method is benefited from a direct discretization approach and…

Numerical Analysis · Mathematics 2020-10-28 Davoud Mirzaei

This paper addresses the problem of obtaining low-order models of fluid flows for the purpose of designing robust feedback controllers. This is challenging since whilst many flows are governed by a set of nonlinear, partial…

This paper introduces a novel meshfree methodology based on Radial Basis Function-Finite Difference (RBF-FD) approximations for the numerical solution of partial differential equations (PDEs) on surfaces of codimension 1 embedded in…

Numerical Analysis · Mathematics 2024-12-20 Víctor Bayona , Argyrios Petras , Cécile Piret , Steven J. Ruuth

The radiative transfer equation (RTE) is a fundamental mathematical model to describe physical phenomena involving the propagation of radiation and its interactions with the host medium. Deterministic methods can produce accurate solutions…

Numerical Analysis · Mathematics 2025-12-18 Kimberly Matsuda , Yanlai Chen , Yingda Cheng , Fengyan Li

Surface Stokes and Navier-Stokes equations are used to model fluid flow on surfaces. They have attracted significant recent attention in the numerical analysis literature because approximation of their solutions poses significant challenges…

Numerical Analysis · Mathematics 2023-09-29 Alan Demlow , Michael Neilan

The Finite Volume method (FVM) is widely adopted in many different applications because of its built-in conservation properties, its ability to deal with arbitrary mesh and its computational efficiency. In this work, we consider the…

Numerical Analysis · Mathematics 2024-07-08 G. Negrini , N. Parolini , M. Verani

The Residual Smooting Scheme (RSS) have been introduced in \cite{AverbuchCohenIsraeli} as a backward Euler's method with a simplified implicit part for the solution of parabolic problems. RSS have stability properties comparable to those of…

Numerical Analysis · Mathematics 2015-06-24 Brachet Matthieu , Chehab Jean-Paul

Reduced order models (ROMs) play a critical role in fluid mechanics by providing low-cost predictions, making them an attractive tool for engineering applications. However, for ROMs to be widely applicable, they must not only generalise…

Machine Learning · Computer Science 2025-05-06 Ismaël Zighed , Nicolas Thome , Patrick Gallinari , Taraneh Sayadi

This paper deals with fast simulations of the haemodynamics in large arteries by considering a reduced model of the associated fluid-structure interaction problem, which in turn allows an additional reduction in terms of the numerical…

Numerical Analysis · Mathematics 2018-01-19 Claudia M. Colciago , Simone Deparis

We present a simple and efficient variational finite difference method for simulating time-dependent Stokes flow in the presence of irregular free surfaces and moving solid boundaries. The method uses an embedded boundary approach on…

Computational Physics · Physics 2011-05-25 Christopher Batty , Robert Bridson

We focus on reducing the computational costs associated with the hydrodynamic stability of solutions of the incompressible Navier-Stokes equations for a Newtonian and viscous fluid in contraction-expansion channels. In particular, we are…

Numerical Analysis · Mathematics 2017-09-01 Giuseppe Pitton , Annalisa Quaini , Gianluigi Rozza

We consider the Navier-Stokes equations in a channel with a narrowing of varying height. The model is discretized with high-order spectral element ansatz functions, resulting in 6372 degrees of freedom. The steady-state snapshot solutions…

Numerical Analysis · Mathematics 2019-04-29 Martin W. Hess , Annalisa Quaini , Gianluigi Rozza