Hydrodynamic forces on a submerged cylinder advancing in water waves of finite depth

1991 ◽  
Vol 224 ◽  
pp. 645-659 ◽  
Author(s):  
G. X. Wu
Keyword(s):  
Water Waves ◽  
Outer Region ◽  
Finite Element Approximation ◽  
Finite Depth ◽  
Horizontal Cylinder ◽  
Hydrodynamic Forces ◽  
Boundary Integral ◽  
Circular Cylinders ◽  
Element Approximation ◽  
Field Equations

The hydrodynamic problem of a submerged horizontal cylinder advancing in regular water waves of finite depth at constant forward speed is analysed by the linearized velocity potential theory. The Green function is first derived. Far-field equations for calculating damping coefficients and exciting forces are obtained. The numerical method used combines a finite-element approximation of the potential in a region surrounding the cylinder with a boundary-integral-equation representation of the outer region. Numerical results for the hydrodynamic forces on submerged circular cylinders and elliptical cylinders are provided.

Hydrodynamic forces on submerged oscillating cylinders at forward speed

1987 ◽  
Vol 414 (1846) ◽  
pp. 149-170 ◽  
Keyword(s):  
Surface Condition ◽  
Outer Region ◽  
Finite Element Approximation ◽  
Boundary Integral ◽  
The Body ◽  
Element Approximation ◽  
Test Cases ◽  
Forward Speed ◽  
Derivatives Of ◽  
Unbounded Fluid

The hydrodynamic problem of submerged oscillating cylinders at forward speed is analysed by linearized potential theory. The numerical method used combines a finite-element approximation of the velocity potential in a region surrounding the cylinder with a boundary integral equation representation of the outer region. This method avoids the calculation of the second-order derivatives of the steady potential due to forward speed, which appear in the body surface condition for the unsteady potential due to the oscillation of the cylinder. Numerical results from the present method for test cases of a circular cylinder in an unbounded fluid and below a free surface are in excellent agreement with the analytical solutions. Further results for elliptic cylinders are provided and the influence of forward speed on the hydrodynamic force on a submerged cylinder is investigated.

Consolidation analysis for unsaturated soils

2004 ◽  
Vol 41 (4) ◽  
pp. 599-612 ◽  
Author(s):  
Enrico Conte
Keyword(s):  
Fourier Transform ◽  
Unsaturated Soils ◽  
Time Integration ◽  
Three Dimensional ◽  
Finite Element Approximation ◽  
Spatial Dimension ◽  
Element Approximation ◽  
Field Equations ◽  
Actual Solution ◽  
The Fourier Transform

This paper deals with the multidimensional consolidation of unsaturated soils when both the air phase and water phase are continuous. Following the approach proposed by D.G. Fredlund and his coworkers, the differential equations governing the coupled and uncoupled consolidation are first derived and then solved numerically. The solution is achieved using a procedure that depends on the transformation of the field equations by using the Fourier transform. This transformation has the effect of reducing a two- or three-dimensional problem to a problem involving only a single spatial dimension. The transformed equations are solved using a finite element approximation that makes use of simple one-dimensional elements. Once the solution in the transformed domain is obtained, the actual solution is achieved by inversion of the Fourier transform. The time integration process is formulated in a stepwise form. Results are presented to point out some aspects of the consolidation in unsaturated soils. Moreover, it is shown that the results obtained using the simple uncoupled theory are of sufficient accuracy for practical purposes.Key words: coupled consolidation, uncoupled consolidation, unsaturated soils, Fourier transform.

scholarly journals Monte Carlo particle-in-cell methods for the simulation of the Vlasov–Maxwell gyrokinetic equations

2015 ◽  
Vol 81 (5) ◽  
Author(s):  
A. Bottino ◽  
E. Sonnendrücker
Keyword(s):  
Finite Element ◽  
Monte Carlo ◽  
Equations Of Motion ◽  
Continuous Distribution ◽  
Finite Element Approximation ◽  
Element Model ◽  
Element Approximation ◽  
Field Equations ◽  
Particle In Cell ◽  
Pic Method

The particle-in-cell (PIC) algorithm is the most popular method for the discretisation of the general 6D Vlasov–Maxwell problem and it is widely used also for the simulation of the 5D gyrokinetic equations. The method consists of coupling a particle-based algorithm for the Vlasov equation with a grid-based method for the computation of the self-consistent electromagnetic fields. In this review we derive a Monte Carlo PIC finite-element model starting from a gyrokinetic discrete Lagrangian. The variations of the Lagrangian are used to obtain the time-continuous equations of motion for the particles and the finite-element approximation of the field equations. The Noether theorem for the semi-discretised system implies a certain number of conservation properties for the final set of equations. Moreover, the PIC method can be interpreted as a probabilistic Monte Carlo like method, consisting of calculating integrals of the continuous distribution function using a finite set of discrete markers. The nonlinear interactions along with numerical errors introduce random effects after some time. Therefore, the same tools for error analysis and error reduction used in Monte Carlo numerical methods can be applied to PIC simulations.

scholarly journals Nonlinear interactions of nearly non-dispersive equatorial shallow-water waves

2020 ◽  
Vol 85 (3) ◽  
pp. 365-384
Author(s):  
Mian Wang ◽  
Zhan Wang ◽  
Hennes Hajduk
Keyword(s):  
Water Waves ◽  
Large Scale ◽  
Multiple Scales ◽  
Wave Interaction ◽  
Finite Element Approximation ◽  
Galerkin Projection ◽  
Primitive Equations ◽  
Element Approximation ◽  
Nonlinear Interactions ◽  
Simplified Models

Abstract This paper is concerned with nonlinear interactions of fundamental equatorial modes. In order to understand the mechanism of large-scale atmospheric motions in the near equator regime—especially the observed wavenumber-frequency spectrum—we develop novel models describing interactions among Kelvin, Yanai and Poincaré waves. Based on the methods of multiple scales and Galerkin projection, the primitive equations can be simplified to model equations which reduce the complexity and cost of computation significantly. Subsequently, the detailed numerical results indicate that wave interactions between the aforementioned modes in the non-dispersive regime depends on initial amplitude and relative phase and that the eastward Yanai wave can be generated from the second Poincaré mode. We also compare the simplified models to an advanced finite element approximation for the primitive equations. The fact that results of the latter are in good agreement, at least qualitatively, with those of the simplified models, indicates that reduced models capture most of the wave interaction mechanisms in the nearly non-dispersive regime.

Radiation and diffraction by a submerged sphere advancing in water waves of finite depth

1995 ◽  
Vol 448 (1932) ◽  
pp. 29-54 ◽  
Keyword(s):  
Water Waves ◽  
Finite Depth ◽  
Multipole Expansion ◽  
The Body ◽  
Field Equations ◽  
Damping Coefficients ◽  
Submerged Sphere ◽  
Added Masses ◽  
Exciting Forces ◽  
Depth Water

A submerged sphere advancing in a regular finite depth water wave at constant forward speed is analysed by linearized velocity potential. The solution is ob­tained by the multipole expansion extended from that developed for zero speed. Numerical results are obtained for wave-making resistance and lift, added masses, damping coefficients and exciting forces. Far field equations are also derived for calculating damping coefficients and exciting forces. They are used to check the results obtained from integrating pressure over the body surface. Excellent agree­ment is found.

Trapping of water waves by submerged plates using hypersingular integral equations

1995 ◽  
Vol 284 ◽  
pp. 359-375 ◽  
Author(s):  
Neil F. Parsons ◽  
P. A. Martin
Keyword(s):  
Integral Equation ◽  
Surface Water ◽  
Water Waves ◽  
Velocity Potential ◽  
Finite Depth ◽  
Circular Cylinders ◽  
Hypersingular Integral Equation ◽  
Flat Plates ◽  
Hypersingular Integral ◽  
Surface Water Waves

The trapping of surface water waves by a thin plate in deep water is reduced to finding non-trivial solutions of a homogeneous, hypersingular integral equation for the discontinuity in velocity potential across the plate. The integral equation is discretized using an expansion-collocation method, involving Chebyshev polynomials of the second kind. A non-trivial solution to the problem is given by the vanishing of the determinant inherent in such a method. Results are given for inclined flat plates, and for curved plates that are symmetric with respect to a line drawn vertically through their centre. Comparisons with published results for horizontal flat plates (in water of finite depth) and for circular cylinders are made.

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