scholarly journals The Method of Fundamental Solutions for Three-Dimensional Nonlinear Free Surface Flows Using the Iterative Scheme

2019 ◽  
Vol 9 (8) ◽  
pp. 1715 ◽  
Author(s):  
Cheng-Yu Ku ◽  
Jing-En Xiao ◽  
Chih-Yu Liu
Keyword(s):  
Free Surface ◽  
Nonlinear Boundary ◽  
Three Dimensional ◽  
Nonlinear Boundary Conditions ◽  
Fundamental Solutions ◽  
Free Surface Flows ◽  
Three Dimensions ◽  
Method Of Fundamental Solutions ◽  
Surface Flows ◽  
Nonlinear Free Surface

In this article, we present a meshless method based on the method of fundamental solutions (MFS) capable of solving free surface flow in three dimensions. Since the basis function of the MFS satisfies the governing equation, the advantage of the MFS is that only the problem boundary needs to be placed in the collocation points. For solving the three-dimensional free surface with nonlinear boundary conditions, the relaxation method in conjunction with the MFS is used, in which the three-dimensional free surface is iterated as a movable boundary until the nonlinear boundary conditions are satisfied. The proposed method is verified and application examples are conducted. Comparing results with those from other methods shows that the method is robust and provides high accuracy and reliability. The effectiveness and ease of use for solving nonlinear free surface flows in three dimensions are also revealed.

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.

A Moving Pseudo-Boundary MFS for Three-Dimensional Void Detection

2013 ◽  
Vol 5 (04) ◽  
pp. 510-527 ◽  
Author(s):  
Andreas Karageorghis ◽  
Daniel Lesnic ◽  
Liviu Marin
Keyword(s):  
Three Dimensional ◽  
Nonlinear Least Squares ◽  
Fundamental Solutions ◽  
Cauchy Data ◽  
Three Dimensions ◽  
Method Of Fundamental Solutions ◽  
Void Detection ◽  
Spherical Parametrization ◽  
Least Squares Minimization

AbstractWe propose a new moving pseudo-boundary method of fundamental solutions (MFS) for the determination of the boundary of a three-dimensional void (rigid inclusion or cavity) within a conducting homogeneous host medium from overdetermined Cauchy data on the accessible exterior boundary. The algorithm for imaging the interior of the medium also makes use of radial spherical parametrization of the unknown star-shaped void and its centre in three dimensions. We also include the contraction and dilation factors in selecting the fictitious surfaces where the MFS sources are to be positioned in the set of unknowns in the resulting regularized nonlinear least-squares minimization. The feasibility of this new method is illustrated in several numerical examples.

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
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