scholarly journals Numerical Bichromatic Wave Generation Using Designed Mass Source Function

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Min-yi Chen ◽  
Hong-sheng Zhang ◽  
En-xian Zhou ◽  
Da-li Xu
Keyword(s):  
Numerical Model ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Intermediate Water ◽  
Mass Source ◽  
Navier Stokes Equations ◽  
Wave Source ◽  
Wave Maker ◽  
Source Wave

A mass source wave-maker method is generalized as the two-wave-source wave-maker method to generate bichromatic waves in the numerical model, whose governing equations are Navier–Stokes equations with the continuity equation. The Fluent software is taken as the calculation platform. In the numerical model, the waves at both the left and right ends of the numerical wave flume are absorbed with the momentum sources added in Navier–Stokes equations. The numerical simulation of bichromatic waves propagation with different frequencies in uniform deep, intermediate, and shallow water has been conducted. The numerical solutions are compared with the theoretical solutions obtained on the basis of Stokes waves theory. The frequency spectrum analyses of the results are conducted and discussed, and the differences between the weakly nonlinear theoretical solutions and the fully nonlinear numerical results are investigated in detail. It is found that the numerical model can effectively simulate the nonlinear effect of bichromatic waves in water with different depths, and the theoretical solutions only adapt the deep and intermediate water. The results indicate that the present numerical model is valuable in the aspect of practical application.

A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar
Keyword(s):  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Surface Geometry ◽  
Navier Stokes Equations ◽  
S Waves ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

Numerical Modeling of Seabed Response to Combined Wave-Current Loading

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
J.-S. Zhang ◽  
Y. Zhang ◽  
C. Zhang ◽  
D.-S. Jeng
Keyword(s):  
Numerical Modeling ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Laboratory Measurements ◽  
Navier Stokes Equations ◽  
Closure Scheme ◽  
Waves And Currents ◽  
Current Interaction ◽  
Wave Maker ◽  
Current Loading

In this paper, a numerical model is developed to study the dynamic response of a porous seabed to combined wave-current loadings. While the Reynolds-averaged Navier–Stokes equations with k-ε turbulence closure scheme and internal wave-maker function are solved for the phenomenon of wave-current interaction, Biot's poro-elastic “u-p” model is adopted for the seabed response. After validated by the laboratory measurements, this model is applied for the investigation of the effects of waves and currents on the wave-current induced pore pressures. Furthermore, the effects of currents on maximum liquefaction depths of a porous seabed is examined, and it is concluded that the opposite currents will increase the liquefaction depth up to 30% of that without currents.

NUMERICAL SOLUTIONS OF 2D AND 3D SLAMMING PROBLEMS

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
Q Yang ◽  
W Qiu
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Type Equation ◽  
The Body ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Highly Nonlinear ◽  
2D And 3D

Slamming forces on 2D and 3D bodies have been computed based on a CIP method. The highly nonlinear water entry problem governed by the Navier-Stokes equations was solved by a CIP based finite difference method on a fixed Cartesian grid. In the computation, a compact upwind scheme was employed for the advection calculations and a pressure-based algorithm was applied to treat the multiple phases. The free surface and the body boundaries were captured using density functions. For the pressure calculation, a Poisson-type equation was solved at each time step by the conjugate gradient iterative method. Validation studies were carried out for 2D wedges with various deadrise angles ranging from 0 to 60 degrees at constant vertical velocity. In the cases of wedges with small deadrise angles, the compressibility of air between the bottom of the wedge and the free surface was modelled. Studies were also extended to 3D bodies, such as a sphere, a cylinder and a catamaran, entering calm water. Computed pressures, free surface elevations and hydrodynamic forces were compared with experimental data and the numerical solutions by other methods.

scholarly journals Experimental and Simulation Study on Validating a Numerical Model for CO2 Density-Driven Dissolution in Water

Water ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 738
Author(s):  
Holger Class ◽  
Kilian Weishaupt ◽  
Oliver Trötschler
Keyword(s):  
Carbon Dioxide ◽  
Numerical Model ◽  
Stokes Equations ◽  
Onset Time ◽  
Navier Stokes ◽  
Grid Refinement ◽  
Navier Stokes Equations ◽  
Laboratory Flume ◽  
Diffusive Processes ◽  
Color Indicator

Carbon dioxide density-driven dissolution in a water-filled laboratory flume of the dimensions 60 cm length, 40 cm height, 1 cm thickness, was visualized using a pH-sensitive color indicator. We focus on atmospheric pressure conditions, like in caves where CO2 concentrations are typically higher. Varying concentrations of carbon dioxide were applied as boundary conditions at the top of the experimental setup, leading to the onset of convective fingering at differing times. The data were used to validate a numerical model implemented in the numerical simulator DuMux. The model solves the Navier–Stokes equations for density-induced water flow with concentration-dependent fluid density and a transport equation, including advective and diffusive processes for the carbon dioxide dissolved in water. The model was run in 2D, 3D, and pseudo-3D on two different grids. Without any calibration or fitting of parameters, the results of the comparison between experiment and simulation show satisfactory agreement with respect to the onset time of convective fingering, and the number and the dynamics of the fingers. Grid refinement matters, in particular, in the uppermost part where fingers develop. The 2D simulations consistently overestimated the fingering dynamics. This successful validation of the model is the prerequisite for employing it in situations with background flow and for a future study of karstification mechanisms related to CO2-induced fingering in caves.

Numerical Modelling of Circulation in Lake Sperillen, Norway

2000 ◽  
Vol 31 (1) ◽  
pp. 57-72 ◽  
Author(s):  
N. R. B. Olsen ◽  
D. K. Lysne
Keyword(s):  
Numerical Model ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Field Measurements ◽  
Navier Stokes ◽  
Water Current ◽  
Simple Method ◽  
Vertical Temperature Profile ◽  
Navier Stokes Equations ◽  
Good Agreement

A three-dimensional numerical model was used to model water circulation and spatial variation of temperature in Lake Sperillen in Norway. A winter situation was simulated, with thermal stratification and ice cover. The numerical model solved the Navier-Stokes equations on a 3D unstructured non-orthogonal grid with hexahedral cells. The SIMPLE method was used for the pressure coupling and the k-ε model was used to model turbulence, with a modification for density stratification due to the vertical temperature profile. The results were compared with field measurements of the temperature in the lake, indicating the location of the water current. Reasonably good agreement was found.

scholarly journals Mathematical Model for the Electrokinetic Instability of Electrolyte Flow

2019 ◽  
Vol 224 ◽  
pp. 02003
Author(s):  
Andrey Shobukhov
Keyword(s):  
Electric Potential ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Steady State Solution ◽  
Stability Loss ◽  
Navier Stokes ◽  
Ion Distribution ◽  
Navier Stokes Equations ◽  
Dilute Aqueous Solution

We study a one-dimensional model of the dilute aqueous solution of KCl in the electric field. Our model is based on a set of Nernst-Planck-Poisson equations and includes the incompressible fluid velocity as a parameter. We demonstrate instability of the linear electric potential variation for the uniform ion distribution and compare analytical results with numerical solutions. The developed model successfully describes the stability loss of the steady state solution and demonstrates the emerging of spatially non-uniform distribution of the electric potential. However, this model should be generalized by accounting for the convective movement via the addition of the Navier-Stokes equations in order to substantially extend its application field.

scholarly journals Development of An Integrated Numerical Model for Simulating Wave Interaction with Permeable Submerged Breakwaters Using Extended Navier–Stokes Equations

2020 ◽  
Vol 8 (2) ◽  
pp. 87 ◽  
Author(s):  
Paran Pourteimouri ◽  
Kourosh Hejazi
Keyword(s):  
Porous Medium ◽  
Wave Propagation ◽  
Numerical Model ◽  
Analytical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Stokes Wave ◽  
Navier Stokes Equations ◽  
Numerical Predictions ◽  
The Impact

An integrated two-dimensional vertical (2DV) model was developed to investigate wave interactions with permeable submerged breakwaters. The integrated model is capable of predicting the flow field in both surface water and porous media on the basis of the extended volume-averaged Reynolds-averaged Navier–Stokes equations (VARANS). The impact of porous medium was considered by the inclusion of the additional terms of drag and inertia forces into conventional Navier–Stokes equations. Finite volume method (FVM) in an arbitrary Lagrangian–Eulerian (ALE) formulation was adopted for discretization of the governing equations. Projection method was utilized to solve the unsteady incompressible extended Navier–Stokes equations. The time-dependent volume and surface porosities were calculated at each time step using the fraction of a grid open to water and the total porosity of porous medium. The numerical model was first verified against analytical solutions of small amplitude progressive Stokes wave and solitary wave propagation in the absence of a bottom-mounted barrier. Comparisons showed pleasing agreements between the numerical predictions and analytical solutions. The model was then further validated by comparing the numerical model results with the experimental measurements of wave propagation over a permeable submerged breakwater reported in the literature. Good agreements were obtained for the free surface elevations at various spatial and temporal scales, velocity fields around and inside the obstacle, as well as the velocity profiles.

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