scholarly journals SOLITARY WAVES PASSING OVER SUBMERGED BREAKWATERS

1988 ◽  
Vol 1 (21) ◽  
pp. 45
Author(s):  
Mark Cooker ◽  
Howell Peregrine
Keyword(s):  
Solitary Waves ◽  
Integral Method ◽  
Velocity Potential ◽  
Fluid Motion ◽  
Unsteady Motion ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Sea Bed ◽  
Exact Boundary

A method is described for the computation of the two-dimensional unsteady motion of a solitary wave passing over submerged breakwaters. Far from the breakwater the fluid is assumed static and the sea bed is level. The fluid motion is assumed to be irrotational, incompressible and inviscid. The exact boundary conditions at the free surface and the impermeable bed are satisfied. Laplace's equation for the velocity potential is solved using a boundary integral method. Numerical results are reported which show the variety of ways in which solitary waves are distorted when they encounter submerged breakwaters.

A boundary integral method for the simulation of two-dimensional particle coarsening

1986 ◽  
Vol 1 (2) ◽  
pp. 117-144 ◽  
Author(s):  
G. B. McFadden ◽  
P. W. Voorhees ◽  
R. F. Boisvert ◽  
D. I. Meiron
Keyword(s):  
Integral Method ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Particle Coarsening

scholarly journals Exact Boundary Derivative Formulation for Numerical Conformal Mapping Method

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
Wei-Lin Lo ◽  
Nan-Jing Wu ◽  
Chuin-Shan Chen ◽  
Ting-Kuei Tsay
Keyword(s):  
Conformal Mapping ◽  
Integral Method ◽  
Mapping Method ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Width Ratio ◽  
Rectangular Region ◽  
Exact Boundary ◽  
Cauchy Riemann ◽  
Specific Length

Conformal mapping is a useful technique for handling irregular geometries when applying the finite difference method to solve partial differential equations. When the mapping is from a hyperrectangular region onto a rectangular region, a specific length-to-width ratio of the rectangular region that fitted the Cauchy-Riemann equations must be satisfied. In this research, a numerical integral method is proposed to find the specific length-to-width ratio. It is conventional to employ the boundary integral method (BIEM) to perform the conformal mapping. However, due to the singularity produced by the BIEM in seeking the derivatives on the boundaries, the transformation Jacobian determinants on the boundaries have to be evaluated at inner points instead of directly on the boundaries. This approximation is a source of numerical error. In this study, the transformed rectangular property and the Cauchy-Riemann equations are successfully applied to derive reduced formulations of the derivatives on the boundaries for the BIEM. With these boundary derivative formulations, the Jacobian determinants can be evaluated directly on the boundaries. Furthermore, the results obtained are more accurate than those of the earlier mapping method.

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