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The answer to this question is more related to an explicit implementation rather than the SPH material model itself. In general, CFL or Courant criteria limits the time step of an explicit calculation. It puts a limit on dt that roughly says that the signal cannot travel more than 1 element width in any time step to preserve a sense of history of that signal. i.e., dt < dx/C C= sound speed of the material dx = element width The bigger C is the smaller dt is. C is proportional to K0 ==> Bigger K0 ==> bigger C ==> smaller dt. So, in an SPH simulation, the idea is that we can artificially make the fluid “softer” by lowering its bulk modulus (to achieve bigger dt) as long as we do not change the apparent compressibility of the fluid, hence, we are not changing the physics of the flow. Checking the rho is a way to make sure we do not change the compressibility of the fluid.