I wonder to what extent simulation can reliably test the mechanical and detonation aspects? I always imagined simulation assumed you have an explosion and you want to see the effect.

If you can’t run physical experiments to adjust your models, you are limited with what you can do in terms of new designs. I would assume manufacturing and maintenance of nuclear warheads is very conservative with their designs.

That's where the NIF comes into play, the National Ignition Facility. They use lasers to generate conditions similar to a nuclear explosion for testing purposes.