What is the best method to solve a 2D water wave equation?

[hunt]

Help!anyone can help me?

I'm currently doing the 2D water waves simulations.Before that I have to solve the 2 dimensional water wave equation (a kind of second order partial differential equation -hyperbolic equation).what method can i use to solve the equation? i m thinking to use the finite difference method?is it suitable?any comment on that?

is ther any other method can be used?how about the pros and cons for the above solution and methods? thank you for helping ...

 

[saltydog]

I'm currently doing the 2D water waves simulations.Before that I have to solve the 2 dimensional water wave equation (a kind of second order partial differential equation -hyperbolic equation).what method can i use to solve the equation? i m thinking to use the finite difference method?is it suitable?any comment on that?

is ther any other method can be used?how about the pros and cons for the above solution and methods? thank you for helping ...

Finite-difference can be applied to hyperbolic PDEs in multiple dimensions. However, if the PDE is relatively simple, separation of variables can work too. Suppose transforms would also do. Me, after looking into the stability considerations of finite differences applied to this problem, I'd work a simpler one analytically, then debug the finite difference method by comparing the output to the analytical solution, then solve the real one using the bug-free method, then calculate all the derivatives numerically for some random points or a range, and back-substitute those results into the PDE to see how close it is. That's just me though.

So what's the IBVP?