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Shallow water waves model in coefficient PDE or general PDE

Posted May 14, 2013, 7:49 a.m. EDT Computational Fluid Dynamics (CFD), Microfluidics, Modeling Tools & Definitions, Parameters, Variables, & Functions, Studies & Solvers Version 4.3a 2 Replies

Muamer Kadic
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Dear All,
I want to solve the Shallow water waves equations in PDE module in 2D. h is the water elevation, U and V the velocity components along x and y.

How can I implement an incoming pulse in the times domain. Coming from the left on the structure.

If I use the initial conditions, I can specify the shape at given time but I don t see any way of defining for example a incoming wave from the left to the right with a shape like:
h(x,y,t)=exp((t-t0)^2)sin(2*pi*freqt)

Best regards
Muamer
2 Replies Last Post May 21, 2013, 10:28 a.m. EDT
Eric Favre COMSOL Employee

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Posted: 1 decade ago May 17, 2013, 9:50 a.m. EDT
Hello Muamer,

Allow me to rephrase your question to these general statements:

- initial conditions control the solution in space at t=0 only.
- boundary conditions control the solution in space and time at any time.
Dirichlet control the unknown.
Neumann control the derivative of the unknow (or rather the normal component of what you have put under the divergence operator).

This is useful to have consistency (I mean no discontinuity in time) between initial and boundary conditions when your boundary conditions are expressed with respect to the unknown itself (Dirichlet) : otherwise you introduce a discontinuity that is (often) non physical and that you might need to damp out later (unless shock or specific applications).
If your boundary conditions are "fluxes" (derivative of the unknown = Neumann bc), then you can introduce discontinuity, this is (often) correct.

Shallow water equations are directly integrated into CFD or Microfluidics module.

You have an example of Shallow water formulation within COMSOL, Model Library (no module required). The constraint is time independant but that should be really easy to give a funciton of time for the elevation. Just write it in a new Dirichlet boundary condition!

Good luck,
Eric
Hello Muamer, Allow me to rephrase your question to these general statements: - initial conditions control the solution in space at t=0 only. - boundary conditions control the solution in space and time at any time. Dirichlet control the unknown. Neumann control the derivative of the unknow (or rather the normal component of what you have put under the divergence operator). This is useful to have consistency (I mean no discontinuity in time) between initial and boundary conditions when your boundary conditions are expressed with respect to the unknown itself (Dirichlet) : otherwise you introduce a discontinuity that is (often) non physical and that you might need to damp out later (unless shock or specific applications). If your boundary conditions are "fluxes" (derivative of the unknown = Neumann bc), then you can introduce discontinuity, this is (often) correct. Shallow water equations are directly integrated into CFD or Microfluidics module. You have an example of Shallow water formulation within COMSOL, Model Library (no module required). The constraint is time independant but that should be really easy to give a funciton of time for the elevation. Just write it in a new Dirichlet boundary condition! Good luck, Eric
Muamer Kadic
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Posted: 1 decade ago May 21, 2013, 10:28 a.m. EDT
Dear Eric,
thanks for your email.
I have already looked into the shallow water model which is in 1d. I have tried to extrapolated the equations to 2d (as in my attached file) but it seems that something is not converging.
Regarding the CFD modules...I would be happy to use it but which one can I use to simulate non linear waves such as solitons (tsunami). The idea of using the shallow water model was to consider a 3d problem but solving a 2d equation...

Best regards
Muamer


Dear Eric, thanks for your email. I have already looked into the shallow water model which is in 1d. I have tried to extrapolated the equations to 2d (as in my attached file) but it seems that something is not converging. Regarding the CFD modules...I would be happy to use it but which one can I use to simulate non linear waves such as solitons (tsunami). The idea of using the shallow water model was to consider a 3d problem but solving a 2d equation... Best regards Muamer

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