Comments on descriptions in chapter 1

[Michael Zingale]

1. Incompressible flows are described as $\partial \rho/\partial t = 0$, but there are variable-density incompressible flows (e.g. used for incompressible Rayleigh-Taylor simulations). I think a more common definition is $D\rho/Dt = 0$ which means the density of a fluid element doesn’t change along streamlines (no compressibility effects).
2. In the energy conservation section, it is written h = c_p T, but this assumes that the specific heat is constant in temperature (not true for a general equation of state).
3. You should also note that you are assuming that the thermal conductivity, k, is constant
4. In the “Discretization of the Generic Conservation Equation” section, you write x as three-dimensional, but then talk about one-way and two-way, which are one-dimensional concepts. Somewhere it should be said that you are now working in 1-d
5. “descretized” is misspelled in the “Source Term” section

[Sidafa Conde]

spelling mistake: “negnigible” → negligible

[Sidafa Conde]

In the Transient Term section, you miss $dt$ for the integration with respect to time

[Sidafa Conde]

In Advection Term the variable $A_{ip}$ is first introduce with no explanation

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[Sidafa Conde]

In the Linearization, is $P$ the control volume or $V_p$?

[Christopher Thomas DeGroot]

Regarding the issues raised by Michael Zingale:

1. In this case, the special case that I wanted to refer to was constant density flow. You are absolutely right in your definition. I’ve updated the notebook to clarify that I am talking about constant density flows.
2. I’ve clarified that this is only for the case of constant specific heat capacities.
3. This is noted in brackets where it is stated that the thermophysical properties are constant.
4. I’ve clarified that this discussion is referring to a 1d example.
5. Fixed this.

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[Christopher Thomas DeGroot]

I’ve also addressed the issues of Sidafa Conde, except for the last one. The answer is that $P$ denotes the control volume and $V_P$ denotes its volume. Please open another issue if you think this should be further clarified.