I see your distinction now. That is a good classification.
To go back to the low-Mach/incompressible flow model, I have seen series expansions in terms of the Mach number applied to (subsets of) the fluid flow equations, and the low-Mach approximation is found by setting the Mach number to zero. (Ma = v / c, so if c, the speed of sound, approaches infinity, then Ma goes to 0.) So it seems that you can go the other direction to derive equations starting with the goal of modeling a low-Mach flow, but that’s not typically what I see. There’s no “Mach number dial” in the original equations, so you basically have to modify the equations in some way to see what changes as the Mach number goes to zero.
For this entire class of problems, even if there were a “Mach number dial”, you wouldn’t recover the nice mathematical features you want for speed by setting the Mach number to zero in a code that can handle high Mach physics. So, for fluid flow simulations, I don’t think an explicit declaration of infinite sound speed reducing computational time is possible.
From the perspective of someone in a fluid-flow simulation (if such a thing is possible), however, I don’t think the explicit-implicit classification matters. For all someone inside the simulation knows, the model (their “reality”) explicitly uses an infinite acoustic wave speed. This person might falsely conclude that they don’t live in a simulation because their speed of sound appears to be infinite.
I see your distinction now. That is a good classification.
To go back to the low-Mach/incompressible flow model, I have seen series expansions in terms of the Mach number applied to (subsets of) the fluid flow equations, and the low-Mach approximation is found by setting the Mach number to zero. (Ma = v / c, so if c, the speed of sound, approaches infinity, then Ma goes to 0.) So it seems that you can go the other direction to derive equations starting with the goal of modeling a low-Mach flow, but that’s not typically what I see. There’s no “Mach number dial” in the original equations, so you basically have to modify the equations in some way to see what changes as the Mach number goes to zero.
For this entire class of problems, even if there were a “Mach number dial”, you wouldn’t recover the nice mathematical features you want for speed by setting the Mach number to zero in a code that can handle high Mach physics. So, for fluid flow simulations, I don’t think an explicit declaration of infinite sound speed reducing computational time is possible.
From the perspective of someone in a fluid-flow simulation (if such a thing is possible), however, I don’t think the explicit-implicit classification matters. For all someone inside the simulation knows, the model (their “reality”) explicitly uses an infinite acoustic wave speed. This person might falsely conclude that they don’t live in a simulation because their speed of sound appears to be infinite.