Multiscale Analysis and Computation for the Three-Dimensional Incompressible Navier–Stokes Equations [PDF]
Multiscale Modeling & Simulation, 2008 In this paper, we perform a systematic multiscale analysis for the three-dimensional incompressible Navier–Stokes equations with multiscale initial data. There are two main ingredients in our multiscale method. The first one is that we reparameterize the initial data in the Fourier space into a formal two-scale structure. The second one is the use of a
Hou, Thomas Y. +2 more
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Physics-informed neural networks for solving Reynolds-averaged Navier-Stokes equations [PDF]
The Physics of Fluids, 2021 Physics-informed neural networks (PINNs) are successful machine-learning methods for the solution and identification of partial differential equations (PDEs).
Hamidreza Eivazi +3 more
semanticscholar +1 more source
Second-Order Convergence of a Projection Scheme for the Incompressible Navier–Stokes Equations with Boundaries [PDF]
SIAM Journal on Numerical Analysis, 1993 Summary: A rigorous convergence result is given for a projection scheme for the Navier-Stokes equations in the presence of boundaries. The numerical scheme is based on a finite-difference approximation, and the pressure is chosen so that the computed velocity satisfies a discrete divergence-free condition.
Hou, Thomas Y., Wetton, Brian T. R.
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Numerical simulations of the Lagrangian averaged Navier–Stokes equations for homogeneous isotropic turbulence [PDF]
Physics of Fluids, 2003 Capabilities for turbulence calculations of the Lagrangian averaged Navier–Stokes (LANS-α) equations are investigated in decaying and statistically stationary three-dimensional homogeneous and isotropic turbulence. Results of the LANS-α computations are analyzed by comparison with direct numerical simulation (DNS) data and large eddy simulations.
Mohseni, Kamran +3 more
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Boundary Value Problems, 2020 In this paper, we consider the three-dimensional compressible Navier–Stokes equations with density-dependent viscosity and vorticity-slip boundary condition in a bounded smooth domain.
Dandan Ren, Yunting Ding, Xinfeng Liang
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On singularity formation of a 3D model for incompressible Navier–Stokes equations [PDF]
Advances in Mathematics, 2012 33 ...
Hou, Thomas Y., Shi, Zuoqiang, Wang, Shu
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Accuracy and stability of the continuous-time 3DVAR filter for the Navier–Stokes equation [PDF]
Nonlinearity, 2013 The 3DVAR filter is prototypical of methods used to combine observed data with a dynamical system, online, in order to improve estimation of the state of the system. Such methods are used for high dimensional data assimilation problems, such as those arising in weather forecasting.
Blömker, D. +3 more
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Revisiting the Reynolds-averaged Navier–Stokes equations
Open Physics, 2022 This study revisits the Reynolds-averaged Navier–Stokes (RANS) equations and finds that the existing literature is erroneous regarding the primary unknowns and the number of independent unknowns in the RANS. The literature claims that the Reynolds stress
Sun Bohua
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Global well–posedness for the Lagrangian averaged Navier–Stokes (LANS–α) equations on bounded domains [PDF]
Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2001 The Lagrangian averaged Navier-Stokes (LANS-\(\alpha\)) equations for a fluid moving in a bounded region \(\Omega\subset \mathbb{R}^3\) with smooth boundary \(\partial\Omega\) are given by \[ \begin{aligned} &\frac{\partial v}{\partial t}+U^{\alpha}(v)+\nu A v+ v\cdot\nabla v +(1-\alpha^2\Delta)^{-1}\nabla p=0,\\ &\quad \nabla\cdot v=0\qquad \text{in} \
Marsden, Jerrold E., Shkoller, Steve
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The pullback attractor for the 2D g-Navier-Stokes equation with nonlinear damping and time delay
AIMS Mathematics, 2023 In this article, the global well-posedness of weak solutions for 2D non-autonomous g-Navier-Stokes equations on some bounded domains were investigated by the Faedo-Galerkin method.
Xiaoxia Wang, Jinping Jiang
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