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We consider a test problem for Navier-Stokes solvers based on the flow around a cylinder that exhibits chaotic behavior, to examine the behavior of various numerical methods. We choose a range of Reynolds numbers for which the flow is…

Numerical Analysis · Mathematics 2024-08-19 Henry von Wahl , L. Ridgway Scott

Computational fluid dynamics lies at the heart of many issues in science and engineering, but solving the associated partial differential equations remains computationally demanding. With the rise of quantum computing, new approaches have…

We establish a connection between the strong solution to the spatially periodic Navier-Stokes equations and a solution to a system of forward-backward stochastic differential equations (FBSDEs) on the group of volume-preserving…

Probability · Mathematics 2010-01-21 Ana Bela Cruzeiro , Evelina Shamarova

Navier-Stokes equations are significant partial differential equations that describe the motion of fluids such as liquids and air. Due to the importance of Navier-Stokes equations, the development on efficient numerical schemes is important…

Fluid Dynamics · Physics 2022-07-21 Rui Zhang , Peiyan Hu , Qi Meng , Yue Wang , Rongchan Zhu , Bingguang Chen , Zhi-Ming Ma , Tie-Yan Liu

This paper discussed the global existence of the smoothing solution for the Navier-Stokes equations. At first, we construct the theory of the linear equations which is about the unknown four variables functions with constant coefficients.…

Analysis of PDEs · Mathematics 2011-07-05 Jianfeng Wang

A new approach to model order reduction of the Navier-Stokes equations at high Reynolds number is proposed. Unlike traditional approaches, this method does not rely on empirical turbulence modeling or modification of the Navier-Stokes…

Fluid Dynamics · Physics 2013-09-11 Maciej Balajewicz , Earl Dowell , Bernd Noack

In the last three decades, Fourier analysis methods have known a growing importance in the study of linear and nonlinear PDE's. In particular, techniques based on Littlewood-Paley decomposition and paradifferential calculus have proved to…

Analysis of PDEs · Mathematics 2015-07-10 Raphaël Danchin

Many fundamental problems in fluid dynamics are related to the effects of solid boundaries. In general, they install sharp gradients and contribute to the developement of small-scale structures, which are computationally expensive to…

Fluid Dynamics · Physics 2024-12-20 Ciro S. Campolina , Alexei A. Mailybaev

It is a classical problem in fluid dynamics about the stability and instability of different hydrodynamic patterns in various physical settings, in particular in the high Reynolds number limit of laminar flow with boundary layer. However,…

Analysis of PDEs · Mathematics 2023-08-29 Tong Yang , Zhu Zhang

Analysis of the Navier-Stokes equations in the frames of the algebraic approach to systems of partial differential equations (formal theory of differential equations) is presented.

Mathematical Physics · Physics 2022-01-05 V. V. Zharinov

Numerical solvers of the incompressible Navier-Stokes equations have reproduced turbulence phenomena such as the law of the wall, the dependence of turbulence intensities on the Reynolds number, and experimentally observed properties of…

Fluid Dynamics · Physics 2015-06-05 Divakar Viswanath , Ian Tobasco

We develop a novel and efficient iterative scheme for solving incompressible steady Navier-Stokes equations. The method is an adaptation of the Incremental Viscosity Splitting approximation for unsteady flows to steady equations. At each…

Numerical Analysis · Mathematics 2026-05-07 Aziz Takhirov , Driss Yakoubi

Direct methods to obtain global stability modes are restricted by the daunting sizes and complexity of Jacobians encountered in general three-dimensional flows. Jacobian-free iterative approaches such as Arnoldi methods have greatly…

Fluid Dynamics · Physics 2020-07-13 Rajesh Ranjan , S. Unnikrishnan , Datta Gaitonde

This paper gives out the solution of divergent Navier-Stokes equations, and shows that in this case, under a physicalacceptable condition, the solution would be smooth .

Mathematical Physics · Physics 2011-08-23 Yimin Yan

A remarkable feature of fluid dynamics is its relationship with classical dynamics and statistical mechanics. This has motivated in the past mathematical investigations concerning, in a special way, the "derivation" based on kinetic theory,…

A mechanical model and finite element method for the simultaneous solution of Stokes and incompressible Navier-Stokes flows on multiple curved surfaces over a bulk domain are proposed. The two-dimensional surfaces are defined implicitly by…

Computational Engineering, Finance, and Science · Computer Science 2025-10-09 Michael Wolfgang Kaiser , Thomas-Peter Fries

We present a symmetry classification of the linearised Navier-Stokes equations for a two-dimensional unbounded linear shear flow of an incompressible fluid. The full set of symmetries is employed to systematically derive invariant ansatz…

Fluid Dynamics · Physics 2013-10-11 Andreas Nold , Martin Oberlack

We introduce a modified version of the two-dimensional Navier-Stokes equation, preserving energy and momentum of inertia, which is motivated by the occurrence of different dissipation time scales and related to the gradient flow structure…

Mathematical Physics · Physics 2009-11-13 E. Caglioti , M. Pulvirenti , F. Rousset

We explore the utility of the recently proposed alpha equations in providing a subgrid model for fluid turbulence. Our principal results are comparisons of direct numerical simulations of fluid turbulence using several values of the…

chao-dyn · Physics 2009-10-31 Shiyi Chen , Darryl D. Holm , Len G. Margolin , Raoyang Zhang

The paper is concerned with a class of mathematical models for polymeric fluids, which involves the coupling of the Navier-Stokes equations for a viscous, incompressible, constant-density fluid with a parabolic-hyperbolic…

Analysis of PDEs · Mathematics 2016-01-08 Miroslav Bulíček , Piotr Gwiazda , Endre Süli , Agnieszka Świerczewska-Gwiazda