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This paper derives the stochastic homogenization for two dimensional Navier--Stokes equations with random coefficients. By means of weak convergence method and Stratonovich--Khasminskii averaging principle approach, the solution of two…

Analysis of PDEs · Mathematics 2024-12-18 Dong Su , Hui Liu , Yangyang Shi

By using a new bilinear estimate, a pointwise estimate of the generalized Oseen kernel and an idea of fractional bootstrap, we show in this note that solutions to the Navier-Stokes equations with fractional dissipation are analytic in space…

Analysis of PDEs · Mathematics 2007-05-23 Hongjie Dong , Dong Li

High-order time-stepping schemes are crucial for simulating incompressible fluid flows due to their ability to capture complex turbulent behavior and unsteady motion. In this work, we propose a third-order accurate numerical scheme for the…

Numerical Analysis · Mathematics 2025-12-22 Kelong Cheng , Jingwei Sun , Hong Zhang

This paper describes in detail the implementation of a finite element technique for solving the compressible Navier-Stokes equations that is provably robust and demonstrates excellent performance on modern computer hardware. The method is…

Numerical Analysis · Mathematics 2022-02-02 Jean-Luc Guermond , Martin Kronbichler , Matthias Maier , Bojan Popov , Ignacio Tomas

We develop two isogeometric divergence-conforming collocation schemes for incompressible flow. The first is based on the standard, velocity-pressure formulation of the Navier-Stokes equations, while the second is based on the rotational…

Numerical Analysis · Mathematics 2023-04-12 Ryan M. Aronson , John A. Evans

A model of fully developed turbulence of a compressible fluid is briefly reviewed. It is assumed that fluid dynamics is governed by a stochastic version of Navier-Stokes equation. We show how corresponding field theoretic-model can be…

Statistical Mechanics · Physics 2018-10-09 M. Hnatič , N. M. Gulitskiy , T. Lučivjanský , L. Mižišin , V. Škultéty

In this work we design and analyse a Discrete de Rham (DDR) method for the incompressible Navier-Stokes equations. Our focus is, more specifically, on the SDDR variant, where a reduction in the number of unknowns is obtained using…

Numerical Analysis · Mathematics 2024-01-10 Daniele A. Di Pietro , Jerome Droniou , Jia Jia Qian

We study stochastic Navier-Stokes equations in two dimensions with respect to periodic boundary conditions. The equations are perturbed by a nonlinear multiplicative stochastic forcing with linear growth (in the velocity) driven by a…

Numerical Analysis · Mathematics 2019-07-10 Dominic Breit , Alan Dodgson

This paper investigates the two-dimensional stochastic steady-state Navier-Stokes(NS) equations with additive random noise. We introduce an innovative splitting method that decomposes the stochastic NS equations into a deterministic NS…

Numerical Analysis · Mathematics 2025-04-23 Jie Zhu , Yujun Zhu , Ju Ming , Max D. Gunzburger

We propose a stochastic collocation method based on the piecewise constant interpolation on the probability space combined with a finite volume method to solve the compressible Navier-Stokes system at the nodal points. We show convergence…

Numerical Analysis · Mathematics 2021-11-16 Eduard Feireisl , Mária Lukáčová-Medvid'ová

We study the time-dependent Navier-Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion, and…

Numerical Analysis · Mathematics 2026-01-14 Bedřich Sousedík , Randy Price

In this paper we first prove the existence and uniqueness of the solution to the stochastic Navier--Stokes equations on the rotating 2-dimensional sphere. Then we show the existence of an asymptotically compact random dynamical system…

Analysis of PDEs · Mathematics 2014-03-27 Zdzislaw Brzeźniak , Beniamin Goldys , Quoc Thong Le Gia

We propose an efficient, accurate and robust implicit solver for the incompressible Navier-Stokes equations, based on a DG spatial discretization and on the TR-BDF2 method for time discretization. The effectiveness of the method is…

A 3D stochastic Navier-Stokes equation with a suitable non degenerate additive noise is considered. The regularity in the initial conditions of every Markov transition kernel associated to the equation is studied by a simple direct…

Probability · Mathematics 2007-05-23 F. Flandoli , M. Romito

We study the Navier-Stokes equations governing the motion of isentropic compressible fluid in three dimensions driven by a multiplicative stochastic forcing. In particular, we consider a stochastic perturbation of the system as a function…

Analysis of PDEs · Mathematics 2017-01-03 Dominic Breit , Martina Hofmanová

This work presents a novel stabilization strategy for the Galerkin formulation of the incompressible Navier-Stokes equations, developed to achieve high accuracy while ensuring convergence and compatibility with high-order elements on…

Numerical Analysis · Mathematics 2025-09-05 Antonio Blanco-Casares , Vishal Kumar , Daniel Mira , Oriol Lehmkuhl

In this paper we consider a fully discrete numerical method for the unsteady Navier-Stokes equations on a smooth closed stationary surface in $\mathbb{R}^3$. We use the surface finite element method (SFEM) with a generalized Taylor-Hood…

Numerical Analysis · Mathematics 2025-12-03 Charles M. Elliott , Achilleas Mavrakis

It is shown that the incompressible Navier-Stokes equation can be derived from an infinite dimensional mean-field stochastic differential equation.

Mathematical Physics · Physics 2018-03-13 Simon Hochgerner

In this work, we study the reproducing kernel (RK) collocation method for the peridynamic Navier equation. We first apply a linear RK approximation on both displacements and dilatation, then back-substitute dilatation, and solve the…

Numerical Analysis · Mathematics 2020-07-23 Yu Leng , Xiaochuan Tian , Nathaniel A. Trask , John T. Foster

The problems of numerical modeling of viscous incompressible fluid flows are widely considered in computational fluid dynamics. Stationary solutions of boundary value problems for the Navier-Stokes equations exist at large Reynolds numbers,…

Numerical Analysis · Mathematics 2024-10-30 D. V. Lomasov , P. N. Vabishchevich