The comments on the accepted answer of my previous question here have left me with a more general question about accurately capturing shockwaves in fluid calculations.
For the sake of having an example, let's say we have a standing shockwave with a pressure or density ratio of 10:1 measured at two points one unit length apart. Let's also assume that I am attempting to capture it with 1D fluid calculations.
In this case, is the shockwave a true singularity, where infinite mesh refinement at the location of the shockwave always leading to one cell having 10 times the flow variable value of an adjacent cell? Or is it the case that the gradients of flow variables may be several orders of magnitude larger within the area of the shockwave than anywhere else, but are still continuous? Does the answer to the above question depend on the source of the shockwave?
And as a tangent question, assuming that the second case is true, over the one unit length thickness of the shockwave, what would be a good rule of thumb for an initial mesh density? 100 cell? 1000?