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

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The discussion focuses on solving the 2D water wave equation, a hyperbolic partial differential equation. The finite difference method is considered suitable for this type of equation, but alternatives like separation of variables and transforms are also mentioned. Stability considerations are important when applying finite differences, and validating results against simpler analytical solutions is recommended. The conversation also hints at the need for clarity on the initial boundary value problem (IBVP) to proceed effectively. Overall, various methods and their implications for solving the equation are explored.
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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 ...
 
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hunt said:
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. :smile:

So what's the IBVP?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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