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bangerth / helmholtz

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Milestone 1: Verify correctness of the code #5

Closed bangerth closed 3 years ago

bangerth commented 3 years ago

Use a simple pipe with two ports, for which I can write down the exact solution of the problem.

bangerth commented 3 years ago

For a simple cylinder with length L and ports at each of the two ends:

For this case we have:

|   cos(kL)        -j*sin(kL)*Zo |* |P1|  = |P2|
| j*sin(kL)/Zo       -cos(kL)    |  |U1|    |U2|

Where

k  = w/c                w = radian frequency =2*pi*f, c = speed of sound (343 m/s)
L  = length of port(m)
Zo = rho*c/S            rho = density of air (1.18 k/m^3)
S  = pi*(D/2)^2         this is the cross section surface area of the port (m^2)
                        where D is it’s diameter (m)

This equation can be used to verify the numerical solution by using the computed values of P1 and U1 and verify that will produces the same P2 and U2 values generated from the FEA solution.

bangerth commented 3 years ago

Addressed with 71a86ed81457e4203933d74e56d0d1b7b36af7df and several previous commits.