Capstone · Numerical Methods, all of them
Every other lab on this site tells you which method to use. This one doesn't. Here are eight physical problems with no method specified. For each one, pick the tool you'd actually reach for, then say what about the problem decides it. Best answer: two candies. A defensible second choice: one. The right reason: one more.
1 · Pick the method
2 · Justify it: what about this problem decides?
Final scorecard
A capstone drawn from across the site. Every method here has its own lab where you can watch it work, or fail. The briefs, scoring and judgments are original to this exercise.
Choosing a method is rarely about which one is "correct". Most problems can be cracked several ways. It's about which features of the problem rule methods in or out. Is there a time variable, or only space? Is the equation linear, with constant coefficients? Does the geometry line up with a coordinate system? How fine does the grid need to be, and what does that do to the stability limit? Is the system sparse? Do you need numbers, or understanding?
That's why each brief asks for the deciding feature, not just the method. If you can name the feature, you can pick the method for a problem you've never seen. That's the whole point of a capstone.
"Defensible" answers earn a candy because real practice is messy. Explicit time-marching does get the right answer, only after a mountain of tiny steps. Finite differences can handle an airfoil, only less exactly and with more grid pain than a conformal map. Knowing when the second-best tool is good enough, because you already have it and it's understood, is a real engineering skill too.
EngineeringCandy · Capstone · every method on this site, one decision at a time · pick it, justify it, beat it