Showing papers on "Navier–Stokes equations published in 2019"
TL;DR: A data driven approach is presented for the prediction of incompressible laminar steady flow field over airfoils based on the combination of deep Convolutional Neural Network (CNN) and deep Multilayer Perceptron (MLP).
Abstract: In this paper, a data driven approach is presented for the prediction of incompressible laminar steady flow field over airfoils based on the combination of deep Convolutional Neural Network (CNN) and deep Multilayer Perceptron (MLP). The flow field over an airfoil depends on the airfoil geometry, Reynolds number, and angle of attack. In conventional approaches, Navier-Stokes (NS) equations are solved on a computational mesh with corresponding boundary conditions to obtain the flow solutions, which is a time consuming task. In the present approach, the flow field over an airfoil is approximated as a function of airfoil geometry, Reynolds number, and angle of attack using deep neural networks without solving the NS equations. The present approach consists of two steps. First, CNN is employed to extract the geometrical parameters from airfoil shapes. Then, the extracted geometrical parameters along with Reynolds number and angle of attack are fed as input to the MLP network to obtain an approximate model to predict the flow field. The required database for the network training is generated using the OpenFOAM solver by solving NS equations. Once the training is done, the flow field around an airfoil can be obtained in seconds. From the prediction results, it is evident that the approach is efficient and accurate.
164 citations
TL;DR: In this paper, the phase-field moving contact line model with soluble surfactants was derived through the first law of thermodynamics, associated thermodynamic relations and the Onsager variational principle, and the derived thermodynamically consistent model consists of two Cahn-Hilliard type of equations governing the evolution of interface and surfactant concentration.
Abstract: Droplet dynamics on a solid substrate is significantly influenced by surfactants. It remains a challenging task to model and simulate the moving contact line dynamics with soluble surfactants. In this work, we present a derivation of the phase-field moving contact line model with soluble surfactants through the first law of thermodynamics, associated thermodynamic relations and the Onsager variational principle. The derived thermodynamically consistent model consists of two Cahn–Hilliard type of equations governing the evolution of interface and surfactant concentration, the incompressible Navier–Stokes equations and the generalized Navier boundary condition for the moving contact line. With chemical potentials derived from the free energy functional, we analytically obtain certain equilibrium properties of surfactant adsorption, including equilibrium profiles for phase-field variables, the Langmuir isotherm and the equilibrium equation of state. A classical droplet spread case is used to numerically validate the moving contact line model and equilibrium properties of surfactant adsorption. The influence of surfactants on the contact line dynamics observed in our simulations is consistent with the results obtained using sharp interface models. Using the proposed model, we investigate the droplet dynamics with soluble surfactants on a chemically patterned surface. It is observed that droplets will form three typical flow states as a result of different surfactant bulk concentrations and defect strengths, specifically the coalescence mode, the non-coalescence mode and the detachment mode. In addition, a phase diagram for the three flow states is presented. Finally, we study the unbalanced Young stress acting on triple-phase contact points. The unbalanced Young stress could be a driving or resistance force, which is determined by the critical defect strength.
105 citations
TL;DR: A numerical scheme for approximating the incompressible Navier-Stokes equations based on an auxiliary variable associated with the total system energy satisfies a discrete energy stability property in terms of a modified energy and it allows for an efficient solution algorithm and implementation.
87 citations
TL;DR: Benzi and Olshanskii as discussed by the authors presented a preconditioner of augmented Lagrangian type for the two-dimensional stationary incompressible Navigable Navigational System.
Abstract: In [M. Benzi and M. A. Olshanskii, SIAM J. Sci. Comput., 28 (2006), pp. 2095--2113] a preconditioner of augmented Lagrangian type was presented for the two-dimensional stationary incompressible Nav...
70 citations
TL;DR: In this paper, the motion of two contiguous incompressible and viscous fluids is described within the diffuse interface theory by the so-called Model H. The system consists of the Navier-Stokes equations, which...
Abstract: The motion of two contiguous incompressible and viscous fluids is described within the diffuse interface theory by the so-called Model H. The system consists of the Navier--Stokes equations, which ...
70 citations
TL;DR: In this article, the Nusselt number and the Skin fraction coefficient of single and multi-wall carbon nanotubes are compared with the same Nussellt number for single and multilayer nanotube.
Abstract: The main objective of this article is to study the inventive conception of the electrical Magneto hydrodynamics (MHD) rotational flow of Single and Multi-Walled Carbon nanotubes (SWCNTs/MWCNTs) base on the fluids (water, engine oil, ethylene glycol and kerosene oil). The thermal radiation impact is taken to be varying the purpose, to see the concentration as well as the temperature modifications between the nanofluid and the surfaces. Kerosene oil is taken as based nanofluids because of its unique attention due to their advanced thermal conductivities, exclusive features and applications. The fluid flow is assumed in steady state. The basic Navier Stocks equations have been transformed through similarity variables in the form of nonlinear differential equations. The solution of the problem has been obtained through Homotopy Analysis Method (HAM). Results obtained for single and multi-wall carbon nanotubes are compared. Plots have been presented in order to examine how the velocities and temperature profile get affected by various flow parameters. The numerical outputs of the physical properties are shown trough tables. The impact of Skin fraction coefficient and Nusselt number are shown in tables.The main objective of this article is to study the inventive conception of the electrical Magneto hydrodynamics (MHD) rotational flow of Single and Multi-Walled Carbon nanotubes (SWCNTs/MWCNTs) base on the fluids (water, engine oil, ethylene glycol and kerosene oil). The thermal radiation impact is taken to be varying the purpose, to see the concentration as well as the temperature modifications between the nanofluid and the surfaces. Kerosene oil is taken as based nanofluids because of its unique attention due to their advanced thermal conductivities, exclusive features and applications. The fluid flow is assumed in steady state. The basic Navier Stocks equations have been transformed through similarity variables in the form of nonlinear differential equations. The solution of the problem has been obtained through Homotopy Analysis Method (HAM). Results obtained for single and multi-wall carbon nanotubes are compared. Plots have been presented in order to examine how the velocities and temperature profil...
66 citations
01 Jan 2019
TL;DR: In this paper, a hybrid technique called homotopy perturbation Elzaki transform method has been applied to solve Navier-Stokes equation of fractional order and three example problems are solved with a purpose to validate and demonstrate the efficacy of the present method.
Abstract: In this article, a hybrid technique called homotopy perturbation Elzaki transform method has been applied to solve Navier–Stokes equation of fractional order. In the hybrid technique, homotopy perturbation method and Elzaki transform method are amalgamated. Three example problems are solved with a purpose to validate and demonstrate the efficacy of the present method. It is also demonstrated that the results obtained from the present method are in excellent agreement with the results by other methods. It is shown that the proposed method is found to be reliable, efficient and easy to implement for various related problems of science and engineering.
66 citations
TL;DR: In this article, the existence and uniqueness issue for the inhomogeneous incompressible Navier-Stokes equations supplemented with H^1 initial velocity and only bounded nonnegative density was studied.
Abstract: 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 with all the previous works on that topics, we do not require regularity or positive lower bound for the initial density, or compatibility conditions for the initial velocity, and still obtain unique solutions. Those solutions are global in the two-dimensional case for general data, and in the three-dimensional case if the velocity satisfies a suitable scaling invariant smallness condition. As a straightforward application, we provide a complete answer to Lions' question in [25], page 34, concerning the evolution of a drop of incompressible viscous fluid in the vacuum.
65 citations
TL;DR: A novel Hybrid High-Order method for the incompressible Navier–Stokes equations based on a formulation of the convective term including Temam's device for stability is proposed, which supports arbitrary approximation orders on general meshes including polyhedral elements and non-matching interfaces.
54 citations
TL;DR: The stability of the unified nonconforming virtual element scheme for the Navier-Stokes equations with different dimensions and different polynomial degrees is proved based on the choice of a proper velocity and pressure pair.
Abstract: In this paper a unified nonconforming virtual element scheme for the Navier-Stokes equations with different dimensions and different polynomial degrees is described. Its key feature is the treatment of general elements including non-convex and degenerate elements. According to the properties of an enhanced nonconforming virtual element space, the stability of this scheme is proved based on the choice of a proper velocity and pressure pair. Furthermore, we establish optimal error estimates in the discrete energy norm for velocity and the L2 norm for both velocity and pressure. Finally, we test some numerical examples to validate the theoretical results.
52 citations
TL;DR: It is proved that if the local second-order structure function exponents in the inertial range remain positive uniformly in viscosity, then any spacetime L2 weak limit of Leray–Hopf weak solutions of the Navier–Stokes equations on any bounded domain is a weak solution of the Euler equations.
Abstract: We prove that if the local second-order structure function exponents in the inertial range remain positive uniformly in viscosity, then any spacetime $$L^2$$
weak limit of Leray–Hopf weak solutions of the Navier–Stokes equations on any bounded domain $$\Omega \subset \mathbb {R}^d$$
, $$d=2,3$$
is a weak solution of the Euler equations. This holds for both no-slip and Navier friction conditions with viscosity-dependent slip length. The result allows for the emergence of non-unique, possibly dissipative, limiting weak solutions of the Euler equations.
TL;DR: In this article, it was shown that the Navier-Stokes equations, after being scaled appropriately by the small aspect ratio parameter of the physical domain, converge strongly to the primitive equations, globally and uniformly in time, and the convergence rate is of the same order as the aspect ratio.
19 Mar 2019
TL;DR: In this article, the authors show the local in time well-posedness of the Prandtl equations for data with Gevrey 2 regularity in x and Sobolev norm in y. The main novelty of their result is that they do not make any assumption on the structure of the initial data: no monotonicity or hypothesis on the critical points.
Abstract: We show the local in time well-posedness of the Prandtl equations for data with Gevrey 2 regularity in x and Sobolev regularity in y. The main novelty of our result is that we do not make any assumption on the structure of the initial data: no monotonicity or hypothesis on the critical points. Moreover, our general result is optimal in terms of regularity, in view of the ill-posedness result of Gerard-Varet and Dormy (J Am Math Soc 23(2):591–609, 2010).
TL;DR: In this article, the evolution towards a finite-time singularity of the Navier-Stokes equations for flow of an incompressible fluid of kinematic viscosity is considered.
Abstract: The evolution towards a finite-time singularity of the Navier–Stokes equations for flow of an incompressible fluid of kinematic viscosity ) is considered, and it is conjectured on the basis of the above dynamical system that a finite-time singularity can indeed occur in this case.
TL;DR: In this paper, a determining map for recovering the full trajectories from their corresponding coarse mesh spatial trajectories is constructed, and the map is then used to develop a downscaling data assimilation scheme for statistical solutions of the two-dimensional Navier-Stokes equations.
TL;DR: In this article, a solution of coupled fractional Navier-Stokes equation is computed numerically using the proposed q-homotopy analysis transform method (q-HATM), and the solution is found in fast convergent series.
Abstract: In this paper, a solution of coupled fractional Navier–Stokes equation is computed numerically using the proposed q-homotopy analysis transform method (q-HATM), and the solution is found in fast convergent series. The given test examples illustrate the leverage and effectiveness of the proposed technique. The obtained results are demonstrated graphically. The present method handles the series solution in a large admissible domain in an extreme manner. It offers us a modest way to adjust the convergence region of the solution. Results with graphs explicitly reveal the efficiency and capability of the proposed algorithm.
TL;DR: In this article, Anderson acceleration has been used as a strategy for solving the Navier-Stokes equations (NSE), and Anderson-accelerated Picard iterations have been used to solve the NSE.
Abstract: We propose, analyze, and test Anderson-accelerated Picard iterations for solving the incompressible Navier--Stokes equations (NSE). Anderson acceleration has recently gained interest as a strategy ...
TL;DR: In this paper, the authors simulate a high-speed droplet impact on a dry/wet rigid wall to investigate the wall shear flow as well as water hammer after the impact.
Abstract: Physical cleaning techniques are of great concern to remove particulate contamination because of their low environmental impact. One of the promising candidates is based on water jets that often involve fission into droplet fragments. Particle removal is believed to be achieved by droplet-impact-induced wall shear flow. Here, we simulate a high-speed droplet impact on a dry/wet rigid wall to investigate the wall shear flow as well as water hammer after the impact. The problem is modeled by the axisymmetric compressible Navier–Stokes equations and solved by a finite volume method that can capture both shocks and material interface. As an example, we consider the impact of a spherical water droplet (200 µm in diameter) at velocity from 30 to 50 m/s against a dry/wet rigid wall. In our simulation, we can reproduce both acoustic and hydrodynamic events. In the dry wall case, the strong wall shear appears near the moving contact line at the wetted surface. On the other hand, once the wall is covered with the liquid film, the wall shear stress gets weaker as the film thickness increases—a similar trend holds for the water-hammer shock loading at the wall. According to the simulated base flow, we compute hydrodynamic force acting on small particles that are assumed to be attached at the wall, in a one-way-coupling manner. The hydrodynamic force acting on the particles is estimated under Stokes’ assumption and compared to particle adhesion of van der Waals type, enabling us to derive a simple criterion of the particle removal.
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TL;DR: In this paper, almost-sure exponentially fast mixing of passive scalars advected by solutions of the stochastically-forced 2D Navier-Stokes equations and 3D hyper-viscous Stokes equations is deduced.
Abstract: We deduce almost-sure exponentially fast mixing of passive scalars advected by solutions of the stochastically-forced 2D Navier-Stokes equations and 3D hyper-viscous Navier-Stokes equations in $\mathbb T^d$ subjected to non-denegenerate $H^\sigma$-regular noise for any $\sigma$ sufficiently large. That is, for all $s > 0$ there is a deterministic exponential decay rate such that all mean-zero $H^s$ passive scalars decay in $H^{-s}$ at this same rate with probability one. This is equivalent to what is known as \emph{quenched correlation decay} for the Lagrangian flow in the dynamical systems literature. This is a follow-up to our previous work, which establishes a positive Lyapunov exponent for the Lagrangian flow-- in general, almost-sure exponential mixing is much stronger than this. Our methods also apply to velocity fields evolving according to finite-dimensional fluid models, for example Galerkin truncations of Navier-Stokes or the Stokes equations with very degenerate forcing. For all $0 \leq k < \infty $ we exhibit many examples of $C^k_t C^\infty_x$ random velocity fields that are almost-sure exponentially fast mixers.
TL;DR: In this paper, the stationary Stokes and Navier-Stokes equations with non-homogeneous Navier boundary condition were studied from the viewpoint of the friction coefficient α, and the existence of a unique weak solution (and strong) in W 1, p (α) (and W 2, p(α) ) to the linear problem for all 1 p ∞ considering minimal regularity of α, using some inf-sup condition concerning the rotational operator.
TL;DR: In this paper, the wall-normal extent of the large-scale structures modelled by the linearized Navier-Stokes equations subject to stochastic forcing is directly compared to direct numerical simulation (DNS) data.
Abstract: The wall-normal extent of the large-scale structures modelled by the linearized Navier–Stokes equations subject to stochastic forcing is directly compared to direct numerical simulation (DNS) data. A turbulent channel flow at a friction Reynolds number of 𝜏Re𝜏=2000 is considered. We use the two-dimensional (2-D) linear coherence spectrum (LCS) to perform the comparison over a wide range of energy-carrying streamwise and spanwise length scales. The study of the 2-D LCS from DNS indicates the presence of large-scale structures that are coherent over large wall-normal distances and that are self-similar. We find that, with the addition of an eddy viscosity profile, these features of the large-scale structures are captured by the linearized equations, except in the region close to the wall. To further study this coherence, a coherence-based estimation technique, spectral linear stochastic estimation, is used to build linear estimators from the linearized Navier–Stokes equations. The estimator uses the instantaneous streamwise velocity field or the 2-D streamwise energy spectrum at one wall-normal location (obtained from DNS) to predict the same quantity at a different wall-normal location. We find that the addition of an eddy viscosity profile significantly improves the estimation.
TL;DR: In this article, the authors introduce a notion of global weak solution to the Navier-Stokes equations in three dimensions with initial values in the critical homogeneous Besov spaces.
Abstract: We introduce a notion of global weak solution to the Navier–Stokes equations in three dimensions with initial values in the critical homogeneous Besov spaces $${\dot{B}^{-1+\frac{3}{p}}_{p,\infty}}$$
, p > 3. These solutions satisfy a certain stability property with respect to the weak-
$${\ast}$$
convergence of initial conditions. To illustrate this property, we provide applications to blow-up criteria, minimal blow-up initial data, and forward self-similar solutions. Our proof relies on a new splitting result in homogeneous Besov spaces that may be of independent interest.
01 Dec 2019
TL;DR: In this article, it was shown that for a class of smooth solutions of Navier Stokes equations, namely for shear layer profiles which are unstable for Rayleigh equations, this Ansatz is false if we consider solutions with Sobolev regularity.
Abstract: In 1904, Prandtl introduced his famous boundary layer in order to describe the behavior of solutions of incompressible Navier Stokes equations near a boundary as the viscosity goes to 0. His Ansatz was that the solution of Navier Stokes equations can be described as a solution of Euler equations, plus a boundary layer corrector, plus a vanishing error term in $$L^\infty $$ in the inviscid limit. In this paper we prove that, for a class of smooth solutions of Navier Stokes equations, namely for shear layer profiles which are unstable for Rayleigh equations, this Ansatz is false if we consider solutions with Sobolev regularity, in strong contrast with the analytic case, pioneered by Sammartino and Caflisch (Commun Math Phys 192(2)433–461, 1998; Commun Math Phys 192(2)463–491, 1998). Meanwhile we address the classical problem of the nonlinear stability of shear layers near a boundary and prove that if a shear flow is spectrally unstable for Euler equations, then it is non linearly unstable for the Navier Stokes equations provided the viscosity is small enough.
TL;DR: In this paper, Liouville type theorems for the stationary Navier-Stokes equations are proven under certain assumptions, motivated by conditions that appear in Liouvile type theorem for the heat equations with a given divergence free drift.
Abstract: Liouville type theorems for the stationary Navier-Stokes equations are proven under certain assumptions. These assumptions are motivated by conditions that appear in Liouvile type theorems for the heat equations with a given divergence free drift.
TL;DR: In this article, the authors studied numerical schemes for incompressible Navier-Stokes equations using IMEX temporal discretizations, finite element spatial discretization, and equipped with continuous data assimilation.
TL;DR: In this paper, numerical solution of fractional order Navier-Stokes equations in unsteady viscous fluid flow is found using q-homotopy analysis transform scheme.
Abstract: Abstract In this paper, numerical solution of fractional order Navier-Stokes equations in unsteady viscous fluid flow is found using q-homotopy analysis transform scheme. Fractional derivative is considered in Caputo sense. The proposed technique is a blend of q-homotopy analysis scheme and transform of Laplace. It executes well in efficiency and provides h-curves that show convergence range of series solution.
TL;DR: In this article, it is proven that stochastic transport noise provides a bound on vorticity which gives well posedness, with high probability, for sufficiently large noise intensity and sufficiently high spectrum of the noise.
Abstract: The paper is devoted to the open problem of regularization by noise of 3D Navier-Stokes equations. Opposite to several attempts made with additive noise which remained inconclusive, we show here that a suitable multiplicative noise of transport type has a regularizing effect. It is proven that stochastic transport noise provides a bound on vorticity which gives well posedness, with high probability. The result holds for sufficiently large noise intensity and sufficiently high spectrum of the noise.
TL;DR: In this paper, the ill-posedness of the Leray-Hopf weak solutions of the Navier-Stokes equations was shown for the case when the power of the diffusive term (−Δ)γ is γ < 1/3.
Abstract: We prove the ill-posedness for the Leray–Hopf weak solutions of the incompressible and ipodissipative Navier–Stokes equations, when the power of the diffusive term (−Δ)γ is γ<1/3. We constr...
TL;DR: In this article, the optimal enhanced dissipation rate for the 2D linearized Navier-Stokes equations around the bar state called the Kolmogorov flow was solved by developing the hypocoercivity method introduced by Villani.
Abstract: In this paper, we solve Beck and Wayne’s conjecture on the optimal enhanced dissipation rate for the 2-D linearized Navier-Stokes equations around the bar state called the Kolmogorov flow by developing the hypocoercivity method introduced by Villani (2009).
TL;DR: In this paper, the authors considered a nonlinear system which consists of the incompressible Navier-Stokes equations coupled with a convective nonlocal Cahn-Hilliard equation.
Abstract: We consider a nonlinear system which consists of the incompressible Navier–Stokes equations coupled with a convective nonlocal Cahn–Hilliard equation. This is a diffuse interface model which describes the motion of an incompressible isothermal mixture of two (partially) immiscible fluids having the same density. We assume that both the viscosity and mobility functions depend smoothly on the order parameter. Moreover, we assume that the mobility degenerates at the pure phases and that the potential is singular (e.g. of logarithmic type). This system is endowed with a no-slip boundary condition for the (average) velocity and a homogeneous Neumann boundary condition for the chemical potential. Thus the total mass is conserved. In the two-dimensional case, this problem was already analyzed in some joint papers of the first three authors. However, in the present general case, only the existence of a global weak solution, the (conditional) weak–strong uniqueness and the existence of the global attractor were proven. Here we are able to establish the existence of a (unique) strong solution through an approximation procedure based on time discretization. As a consequence, we can prove suitable uniform estimates which allow us to show some smoothness of the global attractor. Finally, we discuss the existence of strong solutions for the convective nonlocal Cahn–Hilliard equation, with a given velocity field, in the three dimensional case as well.