scholarly journals Asymptotic derivation and simulations of a non-local Exner model in large viscosity regime

2021 ◽  
Author(s):  
Emmanuel Audusse ◽  
Léa Boittin ◽  
Martin Parisot
Keyword(s):  
Stokes Equations ◽  
Momentum Equation ◽  
Type Model ◽  
Elliptic Type ◽  
Sediment Layer ◽  
Water Type ◽  
Full Model ◽  
Numerical Resolution ◽  
Viscosity Term ◽  
Non Local

The present paper deals with the modeling and numerical approximation of bed load transport under the action of water. A new shallow water type model is derived from the stratified two-fluid Navier-Stokes equations. Its novelty lies in the magnitude of a viscosity term that leads to a momentum equation of elliptic type. The full model, sediment and water, verifies a dissipative energy balance for smooth solutions. The numerical resolution of the sediment layer is not trivial since the viscosity introduces a non-local term in the model. Adding a transport threshold makes the resolution even more challenging. A schema based on a staggered discretization is proposed for the full model, sediment and water.

scholarly journals Do the Volume-of-Fluid and the Two-Phase Euler Compete for Modeling a Spillway Aerator?

Water ◽  
2021 ◽  
Vol 13 (21) ◽  
pp. 3092
Author(s):  
Lourenço Sassetti Mendes ◽  
Javier L. Lara ◽  
Maria Teresa Viseu
Keyword(s):  
Stokes Equations ◽  
Cost Benefit ◽  
Volume Of Fluid ◽  
Navier Stokes ◽  
Type Model ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Entrained Air ◽  
Computational Resources ◽  
Mesh Convergence

Spillway design is key to the effective and safe operation of dams. Typically, the flow is characterized by high velocity, high levels of turbulence, and aeration. In the last two decades, advances in computational fluid dynamics (CFD) made available several numerical tools to aid hydraulic structures engineers. The most frequent approach is to solve the Reynolds-averaged Navier–Stokes equations using an Euler type model combined with the volume-of-fluid (VoF) method. Regardless of a few applications, the complete two-phase Euler is still considered to demand exorbitant computational resources. An assessment is performed in a spillway offset aerator, comparing the two-phase volume-of-fluid (TPVoF) with the complete two-phase Euler (CTPE). Both models are included in the OpenFOAM® toolbox. As expected, the TPVoF results depend highly on the mesh, not showing convergence in the maximum chute bottom pressure and the lower-nappe aeration, tending to null aeration as resolution increases. The CTPE combined with the k–ω SST Sato turbulence model exhibits the most accurate results and mesh convergence in the lower-nappe aeration. Surprisingly, intermediate mesh resolutions are sufficient to surpass the TPVoF performance with reasonable calculation efforts. Moreover, compressibility, flow bulking, and several entrained air effects in the flow are comprehended. Despite not reproducing all aspects of the flow with acceptable accuracy, the complete two-phase Euler demonstrated an efficient cost-benefit performance and high value in spillway aerated flows. Nonetheless, further developments are expected to enhance the efficiency and stability of this model.

scholarly journals On the spectral stability of soliton-like solutions to a non-local hydrodynamic-type model

2020 ◽  
Vol 80 ◽  
pp. 104998
Author(s):  
Vsevolod A. Vladimirov ◽  
Sergii Skurativskyi
Keyword(s):  
Spectral Stability ◽  
Hydrodynamic Type ◽  
Type Model ◽  
Non Local

scholarly journals Plane poloidal-toroidal decomposition of doubly periodic vector fields. Part 2. The Stokes equations

2005 ◽  
Vol 47 (1) ◽  
pp. 39-50 ◽  
Author(s):  
G. D. McBain
Keyword(s):  
Vector Fields ◽  
Stokes Equations ◽  
Momentum Equation ◽  
Integral Representations ◽  
Navier Stokes ◽  
Field Equations ◽  
Navier Stokes Equations ◽  
Time Discretisation ◽  
Mass Constraint ◽  
Conservation Of Momentum

AbstractWe continue our study of the adaptation from spherical to doubly periodic slot domains of the poloidal-toroidal representation of vector fields. Building on the successful construction of an orthogonal quinquepartite decomposition of doubly periodic vector fields of arbitrary divergence with integral representations for the projections of known vector fields and equivalent scalar representations for unknown vector fields (Part 1), we now present a decomposition of vector field equations into an equivalent set of scalar field equations. The Stokes equations for slow viscous incompressible fluid flow in an arbitrary force field are treated as an example, and for them the application of the decomposition uncouples the conservation of momentum equation from the conservation of mass constraint. The resulting scalar equations are then solved by elementary methods. The extension to generalised Stokes equations resulting from the application of various time discretisation schemes to the Navier-Stokes equations is also solved.

Heat and Mass Transfer Porous Medium Saturated with Compressible Fluid with Boundary Domain Integral Method

2008 ◽  
Vol 273-276 ◽  
pp. 808-813 ◽  
Author(s):  
Janja Kramer ◽  
Renata Jecl ◽  
Leo Škerget
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Heat And Mass Transfer ◽  
Compressible Fluid ◽  
Integral Method ◽  
Stokes Equations ◽  
Numerical Approach ◽  
Momentum Equation ◽  
Navier Stokes ◽  
Domain Integral

A numerical approach to solve a problem of combined heat and mass transfer in porous medium saturated with compressible fluid is presented. Transport phenomena in porous media is described using the modified Navier-Stokes equations, where for the governing momentum equation the Brinkman extended Darcy formulation is used. Governing equations are solved with the Boundary Domain Integral Method, which is an extension of classical Boundary Element Method.

Analysis of Three-Lobe Bearings Having Non-Newtonian Lubricants by a Finite Element Method

1983 ◽  
Vol 7 (1) ◽  
pp. 7-11 ◽  
Author(s):  
D.V. Singh ◽  
R. Sinhasan ◽  
S.P. Tayal
Keyword(s):  
Shear Stress ◽  
Stokes Equations ◽  
Load Capacity ◽  
Navier Stokes ◽  
Shear Strain Rate ◽  
Navier Stokes Equations ◽  
Viscosity Term ◽  
Static Performance ◽  
Iteration Technique ◽  
Element Method

Additives are extensively used in the commercial lubricants to improve their specific qualities. These lubricants are therefore non-Newtonian and their nonlinear relations between shear stress and shear strain rate are generally represented by cubic shear stress laws. The Navier-Stokes equations and the continuity equation in clindrical coordinates, representing the flow-field in the clearance space of each lobe of the three-lobe hydrodynamic journal bearings having Newtonian fluids, are solved by the finie element method using Galerkin’s technique. The solution for non-Newtonian lubricants is obtained by an iteration technique modifying the viscosity term in each iteration. The static performance characteristics have been obtained for both Newtonian and the non-Newtonian lubricants. The load capacity and friction of the bearing decrease with increase in the nonlinearity of the lubricant whereas the end flow is relatively unaffected.

scholarly journals The acoustic impedance of a laminar viscous jet through a thin circular aperture

2019 ◽  
Vol 864 ◽  
pp. 5-44 ◽  
Author(s):  
David Fabre ◽  
Raffaele Longobardi ◽  
Paul Bonnefis ◽  
Paolo Luchini
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Axisymmetric Flow ◽  
Classical Problem ◽  
Base Flow ◽  
Large Reynolds Number ◽  
Linear Perturbation ◽  
Circular Aperture ◽  
Vena Contracta ◽  
Numerical Resolution

The unsteady axisymmetric flow through a circular aperture in a thin plate subjected to harmonic forcing (for instance under the effect of an incident acoustic wave) is a classical problem first considered by Howe (Proc. R. Soc. Lond. A, vol. 366, 1979, pp. 205–223), using an inviscid model. The purpose of this work is to reconsider this problem through a numerical resolution of the incompressible linearized Navier–Stokes equations (LNSE) in the laminar regime, corresponding to $Re=[500,5000]$. We first compute a steady base flow which allows us to describe the vena contracta phenomenon in agreement with experiments. We then solve a linear problem allowing us to characterize both the spatial amplification of the perturbations and the impedance (or equivalently the Rayleigh conductivity), which is a key quantity to investigate the response of the jet to acoustic forcing. Since the linear perturbation is characterized by a strong spatial amplification, the numerical resolution requires the use of a complex mapping of the axial coordinate in order to enlarge the range of Reynolds number investigated. The results show that the impedances computed with $Re\gtrsim 1500$ collapse onto a single curve, indicating that a large Reynolds number asymptotic regime is effectively reached. However, expressing the results in terms of conductivity leads to substantial deviation with respect to Howe’s model. Finally, we investigate the case of finite-amplitude perturbations through direct numerical simulations (DNS). We show that the impedance predicted by the linear approach remains valid for amplitudes up to order $10^{-1}$, despite the fact that the spatial evolution of the perturbations in the jet is strongly nonlinear.

Boundary Layers With Viscous Potential Outer Flows

Volume 1 ◽  
2004 ◽  
Author(s):  
Alireza Najafiyazdi
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Additional Term ◽  
Reynolds Numbers ◽  
Momentum Equation ◽  
Outer Flow ◽  
Bernoulli’S Equation ◽  
Momentum Integral

In this paper we try to derive improved formulations for laminar boundary layers in incompressible flows by using the concept of viscous potential flows, presented in Joseph [1] and Joseph [2], as the outer flow. Bernoulli’s equation is used at the edge of boundary layer to make the basic assumption to deduce the presented formulas. The momentum equation is derived directly from the Navier-Stokes equations and then simplified using an order of magnitude analyze. However an additional term, μ∂2u∞∂x2, remains in the momentum equation to represent the contribution of the viscosity of the outer potential flow at the edge of the boundary layer. The viscosity of the outer viscous flow shows itself also in momentum-integral and energy-integral equations. Numerical results showed that at high Reynolds numbers and low angles of attack the results of the two formulas are almost the same, but for lower Reynolds numbers and higher angles of attack the difference between the results is remarkable.

scholarly journals Tempered fractional LES modeling

2021 ◽  
Vol 932 ◽  
Author(s):  
Mehdi Samiee ◽  
Ali Akhavan-Safaei ◽  
Mohsen Zayernouri
Keyword(s):  
Isotropic Turbulence ◽  
Stokes Equations ◽  
A Priori ◽  
Correlation Coefficients ◽  
Scale Model ◽  
Navier Stokes ◽  
Model Parameters ◽  
Subgrid Scale ◽  
Modelling Framework ◽  
Non Local

The presence of non-local interactions and intermittent signals in the homogeneous isotropic turbulence grant multi-point statistical functions a key role in formulating a new generation of large-eddy simulation (LES) models of higher fidelity. We establish a tempered fractional-order modelling framework for developing non-local LES subgrid-scale models, starting from the kinetic transport. We employ a tempered Lévy-stable distribution to represent the source of turbulent effects at the kinetic level, and we rigorously show that the corresponding turbulence closure term emerges as the tempered fractional Laplacian, $(\varDelta +\lambda )^{\alpha } (\cdot )$ , for $\alpha \in (0,1)$ , $\alpha \neq \frac {1}{2}$ and $\lambda >0$ in the filtered Navier–Stokes equations. Moreover, we prove the frame invariant properties of the proposed model, complying with the subgrid-scale stresses. To characterize the optimum values of model parameters and infer the enhanced efficiency of the tempered fractional subgrid-scale model, we develop a robust algorithm, involving two-point structure functions and conventional correlation coefficients. In an a priori statistical study, we evaluate the capabilities of the developed model in fulfilling the closed essential requirements, obtained for a weaker sense of the ideal LES model (Meneveau, Phys. Fluids, vol. 6, issue 2, 1994, pp. 815–833). Finally, the model undergoes the a posteriori analysis to ensure the numerical stability and pragmatic efficiency of the model.

scholarly journals Self-attenuation of extreme events in Navier–Stokes turbulence

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Dhawal Buaria ◽  
Alain Pumir ◽  
Eberhard Bodenschatz
Keyword(s):  
Rotation Rate ◽  
Stokes Equations ◽  
Fluid Flows ◽  
Local Strain ◽  
Turbulence Theory ◽  
Navier Stokes ◽  
Spontaneous Generation ◽  
Navier Stokes Equations ◽  
Attenuation Mechanism ◽  
Non Local

AbstractTurbulent fluid flows are ubiquitous in nature and technology, and are mathematically described by the incompressible Navier-Stokes equations. A hallmark of turbulence is spontaneous generation of intense whirls, resulting from amplification of the fluid rotation-rate (vorticity) by its deformation-rate (strain). This interaction, encoded in the non-linearity of Navier-Stokes equations, is non-local, i.e., depends on the entire state of the flow, constituting a serious hindrance in turbulence theory and even establishing regularity of the equations. Here, we unveil a novel aspect of this interaction, by separating strain into local and non-local contributions utilizing the Biot-Savart integral of vorticity in a sphere of radius R. Analyzing highly-resolved numerical turbulent solutions to Navier-Stokes equations, we find that when vorticity becomes very large, the local strain over small R surprisingly counteracts further amplification. This uncovered self-attenuation mechanism is further shown to be connected to local Beltramization of the flow, and could provide a direction in establishing the regularity of Navier-Stokes equations.

Existence results for non-local operators of elliptic type

2013 ◽  
Vol 83 ◽  
pp. 82-90 ◽  
Author(s):  
Chuanzhi Bai
Keyword(s):  
Existence Results ◽  
Elliptic Type ◽  
Local Operators ◽  
Non Local
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