In a numerical wave tank reflected waves are seen from the rear wall. What technique can be adopted to minimize this effect?
I am not so familiar with fluid waves, but in electrodynamics there is also a problem of waves being reflected at boundaries. The solution is to use a perfectly matched layer (Jean Berenger, J. Comp. Phys. 114:185–200, 1994). The basic idea is that you add several boundary points that cause the wave to decay rather than reflect. From a quick search, it looks as if the idea has been extended beyond electrodynamics.
Thanks Fabian.....how do i incorporate the Sommerfeld radiation condition. Do i have to write an expression, The CFD code i am using is ANSYS-CFX. Thanks for the journals as well........cheers.....
Thanks Dan
Perfectly matched layer? Does this mean i have to play with the grid size. The idea is good to decay the waves...at the moment i am trying to simulate real sea waves using a numerical ave tank.
The perfectly matched layer means that you choose the properties of the boundary points so that the wave impedance is perfectly matched to the interior points. That way there is no change in impedance at the boundary, and hence no scattering. The grid size doesn't need to change, although I think it takes ~10 boundary points to dampen electromagnetic waves.
It is possible to use the sponge layers (which absorb the reflected waves) near the boundaries. Please see our paper (Yakovenko et al., 2011, J. Fluid Mech., Vol. 677, pp.103-133) for this method application to internal breaking waves, and another paper (Bodony D.J., 2006 J. Comput. Phys., Vol.212, pp.681-702) discussed the theoretical basis of this method.
if I understood you correctly, you need to avoid reflection of shock waves from boundaries of you computation domain. You can use free boundary conditions, just setting "mirrored" physical values (density, pressure, velocity) on outer ghost cells: rho_{n+1}=rho_{n}, rho_{n+2}=rho_{n-1}, etc. It is better to use first-order numerical scheme on boundary cells, so you can just have one ghost cell across the boundary. This will avoid gradients on the boundary. If your boundary has complex shape, you can just write equation for your fluxes with "mirrored" values and get equations for your boundary fluxes. For pure gas dynamics and godunov-type scheme, you will get just pure central physical flux as the result for outer boundary.
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