scholarly journals Martingale solutions and Markov selection of stochastic 3D Navier–Stokes equations with jump

2011 ◽  
Vol 250 (6) ◽  
pp. 2737-2778 ◽  
Author(s):  
Zhao Dong ◽  
Jianliang Zhai
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Markov Selection ◽  
Selection Of ◽  
Martingale Solutions

Numerical Simulation of Vortex Induced Vibration Using the K-ε Model

2006 ◽  
Author(s):  
Juan B. V. Wanderley ◽  
Gisele H. B. Souza ◽  
Carlos Levi
Keyword(s):  
Numerical Simulation ◽  
Stokes Equations ◽  
Body Motion ◽  
Navier Stokes ◽  
Experimental Investigations ◽  
Real Problem ◽  
Navier Stokes Equations ◽  
Vortex Induced Vibration ◽  
Selection Of

Numerical simulations of Vortex Induced Vibration have been failing to duplicate accurately experimental data mostly due to the complexity of the physics involved in the real problem. Therefore, a careful and comprehensive investigation on CFD algorithms is still required to indicate the most suitable numerical scheme to handle such a complicate problem. Grid generation, boundary condition implementation, and coupling between the fluid flow governing equations and body motion equation are known to have strong influence on the qualities of the numerical results. This work presents results obtained from a long-term investigation featuring different CFD methods. The investigations enabled the selection of a very effective algorithm that showed an outstanding agreement between experiment and numerical simulation of the VIV phenomenon. Good agreement is obtained in the entire range of reduced velocity covered by the experimental investigations. The successful algorithm discussed here applies the Beam and Warming implicit scheme to solve the two-dimensional slightly compressible Navier–Stokes equations with the K-ε turbulence model to simulate the turbulent flow at the wake of the cylinder.

A framework for optimising aspects of rotor blades

2011 ◽  
Vol 115 (1165) ◽  
pp. 147-161 ◽  
Author(s):  
C. S. Johnson ◽  
G. N. Barakos
Keyword(s):  
Objective Function ◽  
Stokes Equations ◽  
Rotor Blades ◽  
Navier Stokes ◽  
Computational Framework ◽  
Navier Stokes Equations ◽  
Theoretical Predictions ◽  
Artificial Neural ◽  
Optimisation Methods ◽  
Selection Of

AbstractThis work presents a computational framework for the optimisation of various aspects of rotor blades. The proposed method employs CFD combined with artificial neural networks, employed as metamodels, and optimisation methods based on genetic algorithms. To demonstrate this approach, two examples have been used, one is the optimal selection of 4- and 5-digit NACA aerofoils for rotor sections and the other is the optimisation of linear blade twist for rotors in hover. For each case, an objective function was created and the meta-model was subsequently used to evaluate this objective function during the optimisation process. The obtained results agree with real world design examples and theoretical predictions. For the selected cases, the artificial neural network was found to perform adequately though the results required a substantial amount of data for training. The genetic algorithm was found to be very effective in identifying a set of near-optimal parameters. The main CPU cost was associated with the population of the database necessary for the meta-models and this task required CFD computations based on the Reynolds-averaged Navier-Stokes equations. The framework is general enough to allow for several design or optimisation tasks to be carried out and it is based on open-source code made available by the authors.

scholarly journals On the zeroth law of turbulence for the stochastically forced Navier-Stokes equations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yat Tin Chow ◽  
Ali Pakzad
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Energy Dissipation Rate ◽  
Mean Value ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Additional Hypothesis ◽  
The Mean ◽  
Deterministic Force ◽  
Martingale Solutions

<p style='text-indent:20px;'>We consider the three-dimensional stochastically forced Navier–Stokes equations subjected to white-in-time (colored-in-space) forcing in the absence of boundaries. Upper bounds of the mean value of the time-averaged energy dissipation rate are derived directly from the equations for weak (martingale) solutions. This estimate is consistent with the Kolmogorov dissipation law. Moreover, an additional hypothesis of energy balance implies the zeroth law of turbulence in the absence of a deterministic force.</p>

scholarly journals On weak martingale solutions to a stochastic Allen-Cahn-Navier-Stokes model with inertial effects

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
T. Tachim Medjo
Keyword(s):  
Representation Theorem ◽  
Multiplicative Noise ◽  
Stokes Equations ◽  
Galerkin Approximation ◽  
Navier Stokes ◽  
Inertial Effects ◽  
Navier Stokes Equations ◽  
Martingale Solution ◽  
Skorokhod Representation Theorem ◽  
Martingale Solutions

<p style='text-indent:20px;'>We consider a stochastic Allen-Cahn-Navier-Stokes equations with inertial effects in a bounded domain <inline-formula><tex-math id="M1">\begin{document}$ D\subset\mathbb{R}^{d} $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ d = 2, 3 $\end{document}</tex-math></inline-formula>, driven by a multiplicative noise. The existence of a global weak martingale solution is proved under non-Lipschitz assumptions on the coefficients. The construction of the solution is based on the Faedo-Galerkin approximation, compactness method and the Skorokhod representation theorem.</p>

scholarly journals Hyperviscous stochastic Navier–Stokes equations with white noise invariant measure

2020 ◽  
Vol 20 (06) ◽  
pp. 2040005
Author(s):  
M. Gubinelli ◽  
M. Turra
Keyword(s):  
Invariant Measure ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Absolutely Continuous ◽  
Navier Stokes Equations ◽  
Whole Space ◽  
Martingale Solutions

We prove existence and uniqueness of martingale solutions to a (slightly) hyper-viscous stochastic Navier–Stokes equation in 2d with initial conditions absolutely continuous with respect to the Gibbs measure associated to the energy, getting the results both in the torus and in the whole space setting.

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