[hydraulist]

Hi all,
I'm a new learner of cfd. I'm trying to write matlab code for a below Laplase equation with BC. The doubt i've is, can the boundary condition be time dependent where the governing equation is not? The problem is a liquid sloshing in a tank.
governing equ. del^2*si=0, si - velocity potential function
Bounday conditions: in image
1st is on the liquid free surface
2nd is on other 3 wetted sides.

If these are valid, please give me an idea, how to apply this boundary condition in finite difference formulation of the problem.

Thank you

[FMDenaro]

Originally Posted by hydraulist

Hi all,
I'm a new learner of cfd. I'm trying to write matlab code for a below Laplase equation with BC. The doubt i've is, can the boundary condition be time dependent where the governing equation is not? The problem is a liquid sloshing in a tank.
governing equ. del^2*si=0, si - velocity potential function
Bounday conditions: in image
1st is on the liquid free surface
2nd is on other 3 wetted sides.

If these are valid, please give me an idea, how to apply this boundary condition in finite difference formulation of the problem.

Thank you

Generally, if you set time-dependent BC.s, your problem looks like a parabolic equation

df/dt = K Lap f in V

with f(t,x) =g(t) on dV

however, you can solve a Laplace equation at each time you set the BC.s, representing a set of equilibrium solutions for different BC.s


Said that, your equation is second order in time and the mathematical character depends on g ... you could have ellitpic or hyperbolic equations