Difference between revisions of "Integral Equation for the Finite Depth Green Function at Surface"
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| Line 1: | Line 1: | ||
| + | {{complete pages}} | ||
| + | |||
We want to solve | We want to solve | ||
<center><math> | <center><math> | ||
| Line 4: | Line 6: | ||
\left( | \left( | ||
\alpha\phi(\xi) - w(\xi) | \alpha\phi(\xi) - w(\xi) | ||
| − | \right)d \xi | + | \right)\mathrm{d} \xi |
</math></center> | </math></center> | ||
where | where | ||
| − | G(x,\xi) is the [[Free-Surface Green Function]] for two-dimensional waves, with singularity at | + | <math>G(x,\xi)</math> is the [[Free-Surface Green Function]] for two-dimensional waves, with singularity at |
| − | the water surface. We break the surface into <math>N</math>evenly spaced point | + | the water surface. We break the surface into <math>N</math> evenly spaced point |
<math>x_n = -L = hn</math> where <math>h=2L/N</math> and <math>n=0,1,\dots,N</math> | <math>x_n = -L = hn</math> where <math>h=2L/N</math> and <math>n=0,1,\dots,N</math> | ||
| + | |||
| + | |||
| + | == Matlab Code == | ||
| + | |||
| + | A program to calculate the coefficients for the semi-infinite dock problems can be found here | ||
| + | {{green function surface code}} | ||
| + | |||
| + | === Additional code === | ||
| + | |||
| + | This program requires | ||
| + | * {{free surface dispersion equation code}} | ||
| + | |||
| + | [[Category:Linear Water-Wave Theory]] | ||
| + | [[Category:Pages with Matlab Code]] | ||
Latest revision as of 09:06, 19 August 2010
We want to solve
where [math]\displaystyle{ G(x,\xi) }[/math] is the Free-Surface Green Function for two-dimensional waves, with singularity at the water surface. We break the surface into [math]\displaystyle{ N }[/math] evenly spaced point [math]\displaystyle{ x_n = -L = hn }[/math] where [math]\displaystyle{ h=2L/N }[/math] and [math]\displaystyle{ n=0,1,\dots,N }[/math]
Matlab Code
A program to calculate the coefficients for the semi-infinite dock problems can be found here matrix_G_surface.m
Additional code
This program requires
