Discussion on Venkat & Spaulding: “Numerical Simulation of Nonlinear Free-Surface Flows Generated by a Heaving Body of Arbitrary Cross Section”

1991 ◽  
Vol 35 (03) ◽  
pp. 250-253
Author(s):  
Apostolos Papanikolaou
Keyword(s):  
Free Surface ◽  
Cross Section ◽  
Euler Method ◽  
Free Surface Flows ◽  
Arbitrary Cross Section ◽  
Circular Cylinders ◽  
Published Data ◽  
The Time Domain ◽  
Heave Motion ◽  
Nonlinear Free Surface

A method has been presented recently by Venkat and Spaulding to solve the nonlinear boundary-value problem of oscillating two-dimensional cylinders of arbitrary cross section on the free surface of a fluid. The method relies on a second-order finite-difference technique with a modified Euler method for the time domain and a successive over-relaxation procedure for the spatial domain. The authors compare their numerical results with those of other authors (theoretical and experimental), as they have published data for specialized forms like a wedge, circular cylinders, and ship-like sections in forced heave motion (references [4] to [7] and [22], [23] of the paper).

Numerical Simulation of Nonlinear Free-Surface Flows Generated by a Heaving Body of Arbitrary Cross Section

1990 ◽  
Vol 34 (02) ◽  
pp. 92-104
Author(s):  
N. Kolluru Venkat ◽  
M. L. Spaulding
Keyword(s):  
Free Surface ◽  
Potential Flow ◽  
Euler Method ◽  
Flow Equation ◽  
Free Surface Flows ◽  
Arbitrary Cross Section ◽  
Domain Model ◽  
Dimensionless Frequency ◽  
Surface Boundary ◽  
Nonlinear Free Surface

A two-dimensional potential-flow model is employed to predict the wave and flow fields generated by wedge, circular, and semicircular cylinders and ship-shaped bodies in forced heaving motion. The case of a wedge penetrating still fluid at constant velocity is also studied. The model solves the potential flow equation, including the full nonlinear free-surface boundary conditions on a boundary-fitted coordinate system. The model equations are solved using a second-order finite-difference technique with a modified Euler method for the time domain and a successive over relaxation procedure for the spatial domain. Model predictions for the force coefficients and phase angles and the associated hydrodynamic mass and damping coefficients of the heaving bodies are generally in good agreement with available analytic theories and data for the dimensionless frequency range, 0

A B-Spline Based BEM for Unsteady Free-Surface Flows

1999 ◽  
Vol 43 (01) ◽  
pp. 13-24
Author(s):  
M. Landrini ◽  
G. Grytøyr ◽  
O. M. Faltinsen
Keyword(s):  
Free Surface ◽  
Evolution Equations ◽  
Boundary Integral Equations ◽  
Fluid Dynamic ◽  
Domain Boundary ◽  
Free Surface Flows ◽  
Boundary Integral ◽  
Surface Flows ◽  
B Spline ◽  
Nonlinear Free Surface

Fully nonlinear free-surface flows are numerically studied in the framework of the potential theory. The problem is formulated in terms of boundary integral equations which are solved by means of an arbitrary high-order boundary element method based on B-Spline representation of both the geometry and the fluid dynamic variables along the domain boundary. The solution is stepped forward in time either by following Lagrangian points attached to the free surface or by a less conventional scheme in which evolution equations for the B-Spline coefficients are integrated in time. Numerical examples for inner and outer free-surface flows are shown. The accuracy of the numerical solution is assessed either by checking mass and energy conservation or by comparing with reference solutions. Good results are generally obtained. Extended use of the developed algorithm to more applied problems in the context of naval hydrodynamics is now under development.

scholarly journals Computation of Nonlinear Hydrodynamic Loads on Floating Wind Turbines Using Fluid-Impulse Theory

2015 ◽  
Author(s):  
Godine Kok Yan Chan ◽  
Paul D. Sclavounos ◽  
Jason Jonkman ◽  
Gregory Hayman
Keyword(s):  
Free Surface ◽  
Green Function ◽  
Wind Turbines ◽  
Time Domain ◽  
The Body ◽  
Nonlinear Loads ◽  
Frequency Wave ◽  
Linear And Nonlinear ◽  
The Time Domain ◽  
Nonlinear Free Surface

A hydrodynamics computer module was developed to evaluate the linear and nonlinear loads on floating wind turbines using a new fluid-impulse formulation for coupling with the FAST program. The new formulation allows linear and nonlinear loads on floating bodies to be computed in the time domain. It also avoids the computationally intensive evaluation of temporal and spatial gradients of the velocity potential in the Bernoulli equation and the discretization of the nonlinear free surface. The new hydrodynamics module computes linear and nonlinear loads — including hydrostatic, Froude-Krylov, radiation and diffraction, as well as nonlinear effects known to cause ringing, springing, and slow-drift loads — directly in the time domain. The time-domain Green function is used to solve the linear and nonlinear free-surface problems and efficient methods are derived for its computation. The body instantaneous wetted surface is approximated by a panel mesh and the discretization of the free surface is circumvented by using the Green function. The evaluation of the nonlinear loads is based on explicit expressions derived by the fluid-impulse theory, which can be computed efficiently. Computations are presented of the linear and nonlinear loads on the MIT/NREL tension-leg platform. Comparisons were carried out with frequency-domain linear and second-order methods. Emphasis was placed on modeling accuracy of the magnitude of nonlinear low- and high-frequency wave loads in a sea state. Although fluid-impulse theory is applied to floating wind turbines in this paper, the theory is applicable to other offshore platforms as well.

Exact solutions for a class of nonlinear free surface flows

1991 ◽  
Vol 434 (1892) ◽  
pp. 677-682 ◽  
Keyword(s):  
Free Surface ◽  
Free Boundary ◽  
Infinite System ◽  
Free Stream ◽  
Constant Pressure ◽  
Velocity Ratio ◽  
Mapping Function ◽  
Free Surface Flows ◽  
Surface Flows ◽  
Nonlinear Free Surface

We consider a class of inviscid free surface flows where the free surface is of finite length and in which the pressure on the free boundary p b is different from the free stream pressure p ∞ . The aim of the paper is to determine the shape of the free surface as a function of the velocity ratio parameter λ . The free boundary problem is tackled by seeking a mapping z ═ f (ζ) such that the flow past a circle in the ζ-plane maps to a flow with constant pressure p b on the free surface in the z -plane. The formulation leads to an infinite system of coupled nonlinear equations for the coefficients in the mapping function. Remarkably, the system can be solved exactly to yield two families of free surface flows of the form z ═ ζ + λ 2 /ζ + a ( λ ) ln (ζ + b ( λ )/ζ ─ b ( λ )). The nature of the solutions, their limitations and possible extensions to them are discussed.

Nonlinear free‐surface flows past a submerged inclined flat plate

1991 ◽  
Vol 3 (12) ◽  
pp. 2995-3000 ◽  
Author(s):  
J.‐M. Vanden‐Broeck ◽  
Frédéric Dias
Keyword(s):  
Free Surface ◽  
Flat Plate ◽  
Free Surface Flows ◽  
Surface Flows ◽  
Nonlinear Free Surface

On the Coupling of Incompressible SPH with a Finite Element Potential Flow Solver for Nonlinear Free-Surface Flows

2018 ◽  
Vol 28 (3) ◽  
pp. 248-254 ◽  
Author(s):  
Georgios Fourtakas ◽  
Peter Stansby ◽  
Benedict Rogers ◽  
Steven Lind ◽  
Shiqiang Yan ◽  
...  
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Potential Flow ◽  
Free Surface Flows ◽  
Surface Flows ◽  
Flow Solver ◽  
Incompressible Sph ◽  
Nonlinear Free Surface

Deformation Equations for Non-Circular Cylinders

1960 ◽  
Vol 64 (600) ◽  
pp. 765-766 ◽  
Author(s):  
D. S. Houghton ◽  
D. J. Johns
Keyword(s):  
Cylindrical Shell ◽  
Cross Section ◽  
Explicit Solution ◽  
Lateral Pressure ◽  
Arbitrary Cross Section ◽  
Circular Cylinders ◽  
Pressure Loading ◽  
Elastic Shells ◽  
Linear Problems ◽  
Arbitrary Curvature

As far as is known, no explicit solution exists in the literature for the displacement equations in u, v and w, for a uniform cylinder of arbitrary cross section subjected to a lateral pressure loading. However, the advent of Ref. 1 now makes available an admirable treatise devoted entirely to the analysis of thin elastic shells. The equations developed in this reference apply only to linear problems, i.e. the displacements are assumed to be small in comparison with the thickness of the shell, but they are general enough to include all shells of arbitrary curvature. Unfortunately the generality of these equations inhibits their immediate use to cylindrical shell problems, and it is the purpose of this note to present the essential features of the theory for non-circular cylinders.

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