Adding outflow term to the solver implementation

[zasexton]

Problem

Currently the implementation of the svOneDSolver implicitly assumes no mass flux along the length of vessels (despite the original formulation including such terms wan02 (1).pdf but not in steele03.pdf).

Strong form with outflow term ($\psi$):
$$\dfrac{\partial S}{\partial t} + \dfrac{\partial Q}{\partial z} = -\psi$$

$$\dfrac{\partial Q}{\partial t} + \dfrac{\partial}{\partial z}((1+\delta)\dfrac{Q}{S}) + \dfrac{S}{\rho}\dfrac{\partial p}{\partial z} = Sf + N \dfrac{Q}{S} + \nu \dfrac{\partial^2 Q}{\partial z^2}$$

Solution

We intend to review the assumptions made during construction of the residual and stiffness matrix to ensure that the outflow term is properly included in the implementation (instead of assuming no net mass flux as is currently done).

Additional context

@mrp089 can you assign both @JRao-rgb and @zasexton to this issue

Code of Conduct

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[mrp089]

I wish you two good digging on your archeological expedition! It could be useful to add comments to the terms that you reviewed.

[JRao-rgb]

Also modifying the relevant I/O procedures of the code so the parameters of the outflow function can be set from the input files.