So I'm trying to solve a form of the wave equation for sound produced by a vortex distribution $\vec{\omega}$ convecting at velocity $\vec{v}$ .

$$\left(\frac{1}{c_0^2} \frac{\partial^2}{\partial t^2}-\nabla^2\right)B=\nabla \cdot (\vec{\omega} \wedge \vec{v}) $$

The equation is found in Theory of Vortex Sound by M.S. Howe on page 120. The book formulates the equation in terms of enthalpy as opposed to pressure, I suppose because it takes on a simpler form. I'm trying to solve this equation on a pipe. Does anyone know of a reference that formulates the boundary conditions for the problem in terms of enthalpy, or should I just convert it to pressure?

  • $\begingroup$ Enthalpy is linear in $p$, so I would suspect Neumann and Dirichlet boundary conditions to be easily swapped between the two. Are you using some other BC (e.g., Cauchy)? $\endgroup$
    – Kyle Kanos
    Oct 16, 2014 at 18:53
  • $\begingroup$ @kyle-kanos No I'm just using Neumann and Dirichlet bcs. I think what's confusing about this is I've never really seen enthalpy treated as a field quantity before the way pressure is. I've only seen it treated as a state quantity. So I'm not really sure how to go about doing the conversion. I assume B = p + U*V doesn't hold when you're thinking of enthalpy as a field varying in space. $\endgroup$
    – mdornfe1
    Oct 16, 2014 at 19:03
  • $\begingroup$ I typically use enthalpy for computing the energy component of the Riemann problem in Eulerian hydrodynamics, but I have seen some hydrodynamic codes use enthalpy as a field variable--though I do not believe it is a conservative equation when using enthalpy. $\endgroup$
    – Kyle Kanos
    Oct 16, 2014 at 19:30


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