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chapter2/helmholtz_code.ipynb

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"## Test problem\n",
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"As an example, we will model a plane wave propagating in a tube.\n",
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"While it is a basic test case, the code can be adapted to way more complex problems where velocity and impedance boundary conditions are needed.\n",
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"We will apply a velocity boundary condition $v_n = 0.001$ to one end of the tube and an impedance $Z$ computed with the Delaney-Bazley model,\n",
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"We will apply a velocity boundary condition $v_n = 0.001$ to one end of the tube (for the sake of simplicity, in this basic example, we are ignoring the point source, which can be applied with scifem) and an impedance $Z$ computed with the Delaney-Bazley model,\n",
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"supposing that a layer of thickness $d = 0.02$ and flow resistivity $\\sigma = 1e4$ is placed at the second end of the tube.\n",
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"The choice of such impedance (the one of a plane wave propagating in free field) will give, as a result, a solution with no reflections.\n",
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"\n",

chapter2/helmholtz_code.py

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# ## Test problem
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# As an example, we will model a plane wave propagating in a tube.
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# While it is a basic test case, the code can be adapted to way more complex problems where velocity and impedance boundary conditions are needed.
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# We will apply a velocity boundary condition $v_n = 0.001$ to one end of the tube and an impedance $Z$ computed with the Delaney-Bazley model,
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# We will apply a velocity boundary condition $v_n = 0.001$ to one end of the tube (for the sake of simplicity, in this basic example, we are ignoring the point source, which can be applied with scifem) and an impedance $Z$ computed with the Delaney-Bazley model,
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# supposing that a layer of thickness $d = 0.02$ and flow resistivity $\sigma = 1e4$ is placed at the second end of the tube.
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# The choice of such impedance (the one of a plane wave propagating in free field) will give, as a result, a solution with no reflections.
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#

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