Navier–Stokes equations ≈ Navier–Stokes equations
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Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations Open
Machine-learning fluid flow Quantifying fluid flow is relevant to disciplines ranging from geophysics to medicine. Flow can be experimentally visualized using, for example, smoke or contrast agents, but extracting velocity and pressure fie…
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Deep Learning Methods for Reynolds-Averaged Navier–Stokes Simulations of Airfoil Flows Open
With this study we investigate the accuracy of deep learning models for the inference of Reynolds-Averaged Navier-Stokes solutions. We focus on a modernized U-net architecture, and evaluate a large number of trained neural networks with re…
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Physics-informed neural networks for solving Reynolds-averaged Navier–Stokes equations Open
Physics-informed neural networks (PINNs) are successful machine-learning methods for the solution and identification of partial differential equations. We employ PINNs for solving the Reynolds-averaged Navier–Stokes equations for incompres…
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Virtual Elements for the Navier--Stokes Problem on Polygonal Meshes Open
A family of virtual element methods for the two-dimensional Navier-Stokes equations is proposed and analyzed. The schemes provide a discrete velocity field which is pointwise divergence-free. A rigorous error analysis is developed, showing…
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Finding flows of a Navier–Stokes fluid through quantum computing Open
There is great interest in using quantum computers to efficiently simulate a quantum system’s dynamics as existing classical computers cannot do this. Little attention, however, has been given to quantum simulation of a classical nonlinear…
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Liouville type theorem for stationary Navier–Stokes equations Open
It is shown that any smooth solution to the stationary Navier-Stokes system\nin $R^3$ with the velocity field, belonging globally to $L_6$ and $BM0^{-1}$,\nmust be zero.\n
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Analysis of a hybridizable discontinuous Galerkin method for the steady-state incompressible Navier-Stokes equations Open
We present the first a priori error analysis of the hybridizable discontinuous Galerkin method for the approximation of the Navier-Stokes equations proposed in J. Comput. Phys. vol. 230 (2011), pp. 1147-1170. The method is defined on confo…
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New SAV-pressure correction methods for the Navier-Stokes equations: stability and error analysis Open
We construct new first- and second-order pressure correctionschemes using the scalar auxiliary variable approach for the Navier-Stokes equations. These schemes are linear, decoupled and only require solving a sequence of Poisson type equat…
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A staggered space–time discontinuous Galerkin method for the three-dimensional incompressible Navier–Stokes equations on unstructured tetrahedral meshes Open
In this paper we propose a novel arbitrary high order accurate semi-implicit\nspace-time DG method for the solution of the three-dimensional incompressible\nNavier-Stokes equations on staggered unstructured curved tetrahedral meshes. As\nt…
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The Incompressible Navier‐Stokes Equations in Vacuum Open
We are concerned with the existence and uniqueness issue for the inhomogeneous incompressible Navier‐Stokes equations supplemented with H 1 initial velocity and only bounded nonnegative density . In contrast to all the previous works on th…
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Incompressible fluid problems on embedded surfaces: Modeling and variational formulations Open
Governing equations of motion for a viscous incompressible material surface are derived from the balance laws of continuum mechanics. The surface is treated as a time-dependent smooth orientable manifold of codimension one in an ambient Eu…
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Robust Navier-Stokes method for predicting unsteady flowfield and aerodynamic characteristics of helicopter rotor Open
A robust unsteady rotor flowfield solver CLORNS code is established to predict the complex unsteady aerodynamic characteristics of rotor flowfield. In order to handle the difficult problem about grid generation around rotor with complex ae…
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Regularity of 3D axisymmetric Navier-Stokes equations Open
In this paper, we study the three-dimensional axisymmetric Navier-Stokes system with nonzero swirl. By establishing a new key inequality for the pair $(\frac{ω^{r}}{r},\frac{ω^{θ}}{r})$, we get several Prodi-Serrin type regularity criteria…
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Ill-Posedness of Leray Solutions for the Hypodissipative Navier–Stokes Equations Open
ISSN:1432-0916
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Analysis of fractional multi-dimensional Navier–Stokes equation Open
In this paper, a hybrid method called variational iteration transform method has been implemented to solve fractional-order Navier–Stokes equation. Caputo operator describes fractional-order derivatives. The solutions of three examples are…
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Higher‐order surface FEM for incompressible Navier‐Stokes flows on manifolds Open
Summary Stationary and instationary Stokes and Navier‐Stokes flows are considered on two‐dimensional manifolds, ie, on curved surfaces in three dimensions. The higher‐order surface FEM is used for the approximation of the geometry, velocit…
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Global (weak) solution of the chemotaxis-Navier–Stokes equations with non-homogeneous boundary conditions and logistic growth Open
In biology, the behaviour of a bacterial suspension in an incompressible fluid drop is modelled by the chemotaxis-Navier–Stokes equations. This paper introduces an exchange of oxygen between the drop and its environment and an additionally…
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Optimal Distributed Control of a Nonlocal Cahn--Hilliard/Navier--Stokes System in Two Dimensions Open
We study a diffuse interface model for incompressible isothermal mixtures of two immiscible fluids coupling the Navier--Stokes system with a convective nonlocal Cahn--Hilliard equation in two dimensions of space. We apply recently proved w…
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Discrete Energy-Conservation Properties in the Numerical Simulation of the Navier–Stokes Equations Open
Nonlinear convective terms pose the most critical issues when a numerical discretization of the Navier–Stokes equations is performed, especially at high Reynolds numbers. They are indeed responsible for a nonlinear instability arising from…
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Scaling limit of stochastic 2D Euler equations with transport noises to the deterministic Navier–Stokes equations Open
We consider a family of stochastic 2D Euler equations in vorticity form on the torus, with transport-type noises and L2-initial data. Under a suitable scaling of the noises, we show that the solutions converge weakly to that of the determi…
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Compressible Navier-Stokes system : large solutions and incompressible\n limit Open
Here we prove the existence of global in time regular solutions to the\ntwo-dimensional compressible Navier-Stokes equations supplemented with\narbitrary large initial velocity $v\\_0$ and almost constantdensity\n$\\varrho\\_0$, for large …
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DeepCFD: Efficient Steady-State Laminar Flow Approximation with Deep Convolutional Neural Networks Open
Computational Fluid Dynamics (CFD) simulation by the numerical solution of the Navier-Stokes equations is an essential tool in a wide range of applications from engineering design to climate modeling. However, the computational cost and me…
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Validity of steady Prandtl layer expansions Open
Let the viscosity for the 2D steady Navier‐Stokes equations in the region and with no slip boundary conditions at . For , we justify the validity of the steady Prandtl layer expansion for scaled Prandtl layers, including the celebrated Bla…
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Multi-Scale Deep Neural Network (MscaleDNN) Methods for Oscillatory Stokes Flows in Complex Domains Open
In this paper, we study a multi-scale deep neural network (MscaleDNN) as a meshless numerical method for computing oscillatory Stokes flows in complex domains. The MscaleDNN employs a multi-scale structure in the design of its DNN using ra…
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Asymptotic behavior of random Navier-Stokes equations driven by Wong-Zakai approximations Open
In this paper, we investigate the asymptotic behavior of the solutions of the two-dimensional stochastic Navier-Stokes equations via the stationary Wong-Zakai approximations given by the Wiener shift. We prove the existence and uniqueness …
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Weak pullback attractors for stochastic Navier-Stokes equations with nonlinear diffusion terms Open
This paper is concerned with the asymptotic behavior of the solutions of the two-dimensional stochastic Navier-Stokes equations driven by white noise with nonlinear diffusion terms. We prove the existence and uniqueness of weak pullback me…
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Memory embedded non-intrusive reduced order modeling of non-ergodic flows Open
Generating a digital twin of any complex system requires modeling and computational approaches that are efficient, accurate, and modular. Traditional reduced order modeling techniques are targeted at only the first two, but the novel nonin…
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Energy cascade and intermittency in helically decomposed Navier–Stokes equations Open
We study the nature of the triadic interactions in Fourier space for three-dimensional Navier-Stokes equations based on the helicity content of the participating modes. Using the tool of helical Fourier decomposition we are able to access …
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Bayesian Predictions of Reynolds-Averaged Navier–Stokes Uncertainties Using Maximum a Posteriori Estimates Open
Computational fluid dynamics analyses of high-Reynolds-number flows mostly rely on the Reynolds-averaged Navier–Stokes equations. The associated closure models are based on multiple simplifying assumptions and involve numerous empirical cl…
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Nonuniqueness of weak solutions to the Navier-Stokes equation Open
For initial datum of finite kinetic energy, Leray has proven in 1934 that there exists at least one global in time finite energy weak solution of the 3D Navier-Stokes equations. In this paper we prove that weak solutions of the 3D Navier-S…