Grad school.
It’s paradigmatic that physicists look at a problem and try to distill out the essence of it, you can see this at its best and its worse in The Feynman Lectures on Physics where Feynman seems to find a clever trick to make short work of a problem. He’d spent half a lifetime looking for this sort of trick and makes it look easy, one kind of student appreciates that, another kind thinks it is completely unreasonable to expect that they can pull a rabbit out of a hat on command.
There is a dark art of solving hard problems in physics that isn’t really taught outside of grad school, the problem of simulating the explosion of an atom bomb is one of those problems and so would be modeling the evolution of a star on the main sequence. In either one of those cases your main weapon is the partial differential equation and you aren’t going to find a closed-form solution but you are going to solve it numerically. People were solving problems like the above before they had computers, they did the numerical analysis by hand!
For a problem like that you start out using the technique of dimensional analysis that I learned in high school physics, at the outside of your calculation you’re going to have quantities with dimensions. You will have a handful of those and then many more parameters that are ratios (e.g. if you were modeling the planets in the solar system you would put in the radius of the Earth’s orbit in meters and put the rest of the planets in as ratios, notably you could double the size of the whole system and you could scale the time or gravitational constant accordingly and it would be “the same”)
With that in hand solving the inner problem is a long hard fight, it is not too different in principle from those cases where you can solve in closed form (say prove a spherical shell gravitates like a point on the outside but doesn’t gravitate on the outside) except you are going to use numerical solutions, approximations, and such. Actually you don’t learn very much about how to work at that level in classes in grad school, you learn it the hard way working on your PhD.
If there was something you should read to see how it is done, see “An introduction to the study of stellar structure” by Chandresakar and “Structure and Evolution of the Stars” by Schwarzchild. Those books were written before computers were ubiquitous so they show how you attack hard problems without getting bogged down in how you code it up in FORTRAN.