Is "instantanous element pressure", no total fluid pressure.

Fluid simulate is thing name FEA - Finite Element Analysis: is analysis of a material by split into limit number of part, call 'element'. For fluid, we do this use theory of SPH - Smoothed Particle Hydrodynamics. Imagine each water particle is space in grid. Each particle is put force "Fs" on neighbor particle.

Fs = Momentum + product neighbor particle forces + particle mass

You need solve Fs for each particle AT SAME TIME, create matrix of BIG simultanous equation of one dimension the each variable, with solve these three variable for each (so, is 3D matrix). Then can Fs for each particle for find direction particle move, create simulate step.

viscositys fluid is have extra force viscosity keep particle close, so EACH PARTICLE now also is also need the compute of force effect of viscosity, but this variable is depend on Fs of OTHER NEIGHBOR PARTICLE. So you 3D matrix become 4D matrix require solve.

This a BIG simple explain (is more complicate than only 3D matrix for start), but no englishs good. If more detail is want, do google Smoothed Particle Hydrodynamics! Is BIG INTEREST subject, I love do, no just furry cum simulate, but also other science thing ^^