New trends in ensemble forecast strategy: uncertainty quantification for coarse-grid computational fluid dynamics

V Resseguier, L Li, G Jouan, P Dérian, E Mémin… - … Methods in Engineering, 2021‏ - Springer
Numerical simulations of industrial and geophysical fluid flows cannot usually solve the
exact Navier–Stokes equations. Accordingly, they encompass strong local errors. For some …

[ספר][B] Stochastic partial differential equations in fluid mechanics

F Flandoli, E Luongo - 2023‏ - Springer
These notes originated from a series of lectures given at Waseda University in April–May
2021, supported by Top Global University Project of Waseda University. The first author …

Numerically modeling stochastic Lie transport in fluid dynamics

C Cotter, D Crisan, DD Holm, W Pan… - Multiscale Modeling & …, 2019‏ - SIAM
We present a numerical investigation of stochastic transport in ideal fluids. According to
Holm [Proc. A, 471 (2015)] and Cotter, Gottwald, and Holm [Proc. A, 473 (2017)], the …

From additive to transport noise in 2d fluid dynamics

F Flandoli, U Pappalettera - Stochastics and Partial Differential Equations …, 2022‏ - Springer
Abstract Additive noise in Partial Differential equations, in particular those of fluid
mechanics, has relatively natural motivations. The aim of this work is showing that suitable …

Global existence and non-uniqueness of 3D Euler equations perturbed by transport noise

M Hofmanová, T Lange, U Pappalettera - Probability Theory and Related …, 2024‏ - Springer
We construct Hölder continuous, global-in-time probabilistically strong solutions to 3D Euler
equations perturbed by Stratonovich transport noise. Kinetic energy of the solutions can be …

Sharp nonuniqueness of solutions to stochastic Navier–Stokes equations

W Chen, Z Dong, X Zhu - SIAM Journal on Mathematical Analysis, 2024‏ - SIAM
In this paper we establish a sharp nonuniqueness result for stochastic-dimensional ()
incompressible Navier–Stokes equations. First, for every divergence-free initial condition in …

Scaling limit of stochastic 2D Euler equations with transport noises to the deterministic Navier–Stokes equations

F Flandoli, L Galeati, D Luo - Journal of Evolution Equations, 2021‏ - Springer
We consider a family of stochastic 2D Euler equations in vorticity form on the torus, with
transport-type noises and L^ 2 L 2-initial data. Under a suitable scaling of the noises, we …

[HTML][HTML] Stochastic approaches to deterministic fluid dynamics: a selective review

AB Cruzeiro - Water, 2020‏ - mdpi.com
We present a stochastic Lagrangian view of fluid dynamics. The velocity solving the
deterministic Navier–Stokes equation is regarded as a mean time derivative taken over …

A particle filter for stochastic advection by Lie transport: a case study for the damped and forced incompressible two-dimensional Euler equation

C Cotter, D Crisan, DD Holm, W Pan… - SIAM/ASA Journal on …, 2020‏ - SIAM
In this work, we combine a stochastic model reduction with a particle filter augmented with
tempering and jittering, and apply the combined algorithm to a damped and forced …

Weak well-posedness by transport noise for a class of 2D fluid dynamics equations

L Galeati, D Luo - arxiv preprint arxiv:2305.08761, 2023‏ - arxiv.org
A fundamental open problem in fluid dynamics is whether solutions to $2 $ D Euler
equations with $(L^ 1_x\cap L^ p_x) $-valued vorticity are unique, for some $ p\in [1,\infty) …