scholarly journals Recent Results from Analysis of Flow Structures and Energy Modes Induced by Viscous Wave around a Surface-Piercing Cylinder

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Giancarlo Alfonsi ◽  
Agostino Lauria ◽  
Leonardo Primavera
Keyword(s):  
Water Waves ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Wave Flow ◽  
Ocean Engineering ◽  
Navier Stokes Equations ◽  
Pressure Formulation ◽  
The Subject ◽  
Run Up ◽  
Velocity Pressure

Due to its relevance in ocean engineering, the subject of the flow field generated by water waves around a vertical circular cylinder piercing the free surface has recently started to be considered by several research groups. In particular, we studied this problem starting from the velocity-potential framework, then the implementation of the numerical solution of the Euler equations in their velocity-pressure formulation, and finally the performance of the integration of the Navier-Stokes equations in primitive variables. We also developed and applied methods of extraction of the flow coherent structures and most energetic modes. In this work, we present some new results of our research directed, in particular, toward the clarification of the main nonintuitive character of the phenomenon of interaction between a wave and a surface-piercing cylinder, namely, the fact that the wave exerts its maximum force and exhibits its maximum run-up on the cylindrical obstacle at different instants. The understanding of this phenomenon becomes of crucial importance in the perspective of governing the entity of the wave run-up on the obstacle by means of wave-flow-control techniques.

scholarly journals Resolution and implementation of the nonstationary vorticity velocity pressure formulation of the Navier–Stokes equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mohamed Abdelwahed ◽  
Ebtisam Alharbi ◽  
Nejmeddine Chorfi ◽  
Henda Ouertani
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Optimal Error Estimate ◽  
Optimal Error ◽  
Navier Stokes Equations ◽  
Implicit Euler Scheme ◽  
Numerical Tests ◽  
Pressure Formulation ◽  
Velocity Pressure ◽  
Spectral Discretization

Abstract This paper deals with the iterative algorithm and the implementation of the spectral discretization of time-dependent Navier–Stokes equations in dimensions two and three. We present a variational formulation, which includes three independent unknowns: the vorticity, velocity, and pressure. In dimension two, we establish an optimal error estimate for the three unknowns. The discretization is deduced from the implicit Euler scheme in time and spectral methods in space. We present a matrix linear system and some numerical tests, which are in perfect concordance with the analysis.

Dynamics of Unstable Stokes Waves: A Numerical and Experimental Study

2014 ◽  
Author(s):  
Amin Chabchoub ◽  
Robinson Perić ◽  
Norbert P. Hoffmann
Keyword(s):  
Water Waves ◽  
Stokes Equations ◽  
Rogue Waves ◽  
Surface Flow ◽  
Navier Stokes ◽  
Ocean Engineering ◽  
Navier Stokes Equations ◽  
Stokes Waves ◽  
Finite Volume Approach ◽  
Short Term Prediction

Being an appropriate prototype to describe oceanic rogue waves, the Peregrine breather solution of the nonlinear Schrödinger equation is investigated numerically and experimentally to analyze the dynamics of modulationally unstable Stokes waves. The evolution of the water surface elevation is studied numerically by solving the Navier-Stokes equations using a finite-volume approach and a volume of fluid method. The comparison of the numerical results with wave tank experiments show a very good agreement. The results confirm the ability of the chosen method to model the modulation instability of Stokes waves, in particular, breather dynamics in water waves with high accuracy even up to the onset of breaking. We also investigate the sub-surface flow fields, which may be of significance for the short-term prediction of extreme wave focusing in narrow-banded sea state conditions and therefore, for ocean engineering applications.

scholarly journals Vorticity–velocity–pressure formulation for Navier–Stokes equations

2004 ◽  
Vol 6 (2-3) ◽  
pp. 47-52 ◽  
Author(s):  
Mohamed Amara ◽  
Daniela Capatina-Papaghiuc ◽  
Eliseo Chacón-Vera ◽  
David Trujillo
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Pressure Formulation ◽  
Velocity Pressure

scholarly journals Spectral discretization of time-dependent vorticity–velocity–pressure formulation of the Navier–Stokes equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mohamed Abdelwahed ◽  
Nejmeddine Chorfi
Keyword(s):  
Variational Formulation ◽  
Stokes Equations ◽  
Stokes Problem ◽  
Time Discretization ◽  
Time Dependent ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Pressure Formulation ◽  
Velocity Pressure ◽  
Spectral Discretization

Abstract In this work, we propose a nonstationary Navier–Stokes problem equipped with an unusual boundary condition. The time discretization of such a problem is based on the backward Euler’s scheme. However, the variational formulation deduced from the nonstationary Navier–Stokes equations is discretized using the spectral method. We prove that the time semidiscrete problem and the full spectral discrete one admit at most one solution.

scholarly journals MHD convection ow in a constricted channel

2018 ◽  
Vol 26 (2) ◽  
pp. 267-283
Author(s):  
M. Tezer-Sezgin ◽  
Merve Gürbüz
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Hartmann Number ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Particular Solution ◽  
Laminar Convection ◽  
Long Channel ◽  
Velocity Pressure

Abstract We consider the steady, laminar, convection ow in a long channel of 2D rectangular constricted cross-section under the inuence of an applied magnetic field. The Navier-Stokes equations including Lorentz and buoyancy forces are coupled with the temperature equation and are solved by using linear radial basis function (RBF) approximations in terms of the velocity, pressure and the temperature of the fluid. RBFs are used in the approximation of the particular solution which becomes also the approximate solution of the problem. Results are obtained for several values of Grashof number (Gr), Hartmann number (M) and the constriction ratios (CR) to see the effects on the ow and isotherms for fixed values of Reynolds number and Prandtl number. As M increases, the ow is flattened. An increase in Gr increases the magnitude of the ow in the channel. Isolines undergo an inversion at the center of the channel indicating convection dominance due to the strong buoyancy force, but this inversion is retarded with the increase in the strength of the applied magnetic field. When both Hartmann number and constriction ratio are increased, ow is divided into more loops symmetrically with respect to the axes.

Sign in / Sign up

Export Citation Format

Share Document