Add theory documentation for different numerical methods and physics modules in svFSIplus

[JonathanPham]

Problem

Need to add theory documentation for different numerical methods and physics modules in svFSIplus

Solution

Add theory documentation for different numerical methods and physics modules in svFSIplus

Additional context

No response

Code of Conduct

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[ktbolt]

@JonathanPham It is a good practice to describe in the Issue what work you did and any problems you had.

For example, did you encounter any problems with MathJax ?

[JonathanPham]

For the fluid theory, I converted some Latex documentation I previously wrote in Overleaf over to MathJax. Some issues I encountered:

• for time derivatives, \dot{x} was not working well in MathJax (not sure why), so I used \frac{dx}{dt} instead
• square brackets (\left[...\right]) were not working well in MathJax (not sure why), so I avoided using those
• to write multiple aligned equations in Latex, use \begin{align} ... \end{align}. In MathJax, use \begin{aligned} ... \end{aligned}
• to use curly brackets {...}, use \\{...\\} instead of \{...\}

[JonathanPham]

Additional physics theories that need to be added:

• solid mechanics (struct and ustruct)
• electrophysiology
• heat equation
• advection-diffusion

[JonathanPham]

Additional numerical methods that could be added:

• finite element method overview
• generalized-alpha time integration
• linear solver methods

[ktbolt]

The Fluid mechanics section should just describe the finite element formulation for incompressible flow without all of the Brinkman terms. This just adds a bunch of terms that don't have any meaning for users doing CFD.

As far as I know there is currently no one using flow in porous media. But if we really do want to support it then we should add documentation for it (the Inverse_darcy_permeability parameter is not even documented). We can then add a theory section for it.