# laplacian

I am trying to implement the Boudary Layer Impedance model to approximate thermo-viscous losses at solid boundaries for pressure acoustics frequency domain problems, such as described by Bossart et al. (2003) and also by Kampinga (2010).

The idea is to use an impedance boundary condition at solid walls which is first estimated and then updated based on the current solution iteratively until convergence.

In order to calculate the value of the impedance at the boundaries at each iteration, I have to calculate the tangential wavenumber, which is obtained from the tangential laplacian of the pressure at the boundaries.

First question, I tried to calculate the laplacian on the boundaries using:

sol = pde.getSolution()

g_bnd = grad(sol, where = FunctionOnBound

d_bnd = div(g_bnd)

and I get :

RuntimeError: FinleyAdapterEx

Then, assuming I found a solution to that, this is not the value I am looking for because I need the divergence of the components of the gradient parallel to the boundary only. Do I have access to tangential vectors at boundaries?

Many thanks,

Antoine

Rerences

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Bossart, R., Joly, N., & Bruneau, M. (2003). Hybrid numerical and analytical solutions for acoustic boundary problems in thermo-viscous fluids. Journal of Sound and Vibration, 263(1), 69-84.

Kampinga, R. (2010). Viscothermal acoustics using finite elements. Ph.D. thesis. University of Twente, Enschede, The Netherlands.

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