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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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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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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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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Higher-order in time “quasi-unconditionally stable” ADI solvers for the compressible Navier–Stokes equations in 2D and 3D curvilinear domains [PDF]
Journal of Computational Physics, 2016 This paper introduces alternating-direction implicit (ADI) solvers of higher order of time-accuracy (orders two to six) for the compressible Navier-Stokes equations in two- and three-dimensional curvilinear domains. The higher-order accuracy in time results from 1) An application of the backward differentiation formulae time-stepping algorithm (BDF) in
Bruno, Oscar P., Cubillos, Max
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A Liouville theorem for the planer Navier-Stokes equations with the no-slip boundary condition and its application to a geometric regularity criterion [PDF]
, 2013 We establish a Liouville type result for a backward global solution to the Navier-Stokes equations in the half plane with the no-slip boundary condition. No assumptions on spatial decay for the vorticity nor the velocity field are imposed.
Giga, Yoshikazu +2 more
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Generalized Navier–Stokes equations and soft hairy horizons in fluid/gravity correspondence
Nuclear Physics B, 2021 The fluid/gravity correspondence establishes how gravitational dynamics, as dictated by Einstein's field equations, are related to the fluid dynamics, governed by the relativistic Navier–Stokes equations.
A.J. Ferreira–Martins, R. da Rocha
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