I don't think you need any simulation or other visualization than this:
Every straight ray has to go through the focal point, which for a parabola is a single point. You can construct this point for any parabolic solar oven like this [pdf link].
Every ray coming through this focal point will also leave straight up after hitting the opposite side (if the parabola is big enough). The food (or anything else) is supposed to be placed directly at the place of the focal point.
The design with the bottom parabola part under the focal point replaced with (usually) black box is not very efficient if you are trying to heat directly from rays. Usually such design is meant to heat up the whole box, and the food off of this box.
For direct ray focusing a double parabola design with shared focal point will focus the rays much more efficiently:
The pattern of the rays coming through is of doughnut shape, so it is best to place the food in a small circle. You are also able to further focus these rays into a single point with some lens.
If you really need to plot lot of rays, I suggest using CAD software for this (like freeCAD, etc..), where you are able to easily create geometric entities and constrain them to each other.
You can do the same inside Blender with* Constraints* on bones or empties, but it is much more work to setup. The geometry math is very easy though.
You can also preview the caustic pattern of any curved mirrors, but Cycles is not very efficient for this task. Any bi-directional path-tracing renderer is a better choice.
To make cardboard parabolas with Blender you need the Export: Paper Model plugin. You can create parabola meshes with the bundled Add Extra Objects plugin. There are multiple ways to make parabolas, but I like this one:
- it is an icosphere mesh Shrink Wrapped to parabolic mesh
- it can be disassembled into 5 stackable pieces for easy storage
- I marked 1 possibility of gluing flaps placement on one of the pieces, but the Paper Model plugin can figure this out itself. If the cardboard is thick enough, I believe there is no need for flaps, just cuts to be glued together.
- it can be sprayed with reflective paint (Mirror Spray Paint cca $5), imho much better choice than gluing aluminium to paper
A popular idea is also to use an umbrella..