The Problem Domain
I have a number of network-connected PCs. I want to be able to simulate and replicate the same simple fluid dynamics simulation (E.g. Navier-Stokes), in real-time, between them. That is to say, the same body of fluid will be simulated at the same time in isolation on each PC. They will all have the same starting conditions.
Simple so far I hope. Now, each PC with its own simulation can independently add input into the simulation. For example, one PC may add/subtract some fluid at $xyz$ at time $t$ of its own simulation. I need to be able to replicate that input to all other PCs and simulations so they each stay in sync with each other.
I suppose to summarize in other words - I would like to run a single fluid dynamics simulation across a number of network-connected PCs in real-time. I cannot simply replicate the resulting simulation data to all other PCs as the latency and bandwidth requirements would be too great and all other PCs would lag behind. They each need to be in sync as much as possible.
My question here is in regards to the fluid dynamics equation: Is it possible to simulate fluid dynamics that can take input at time $t$, that may be in the past by the time the simulation gets the input, and take that into account?
Note: When I say input I mean a change in the simulation environment be it a change to the container the fluid is held in, a change in forces or a change in fluid volume.
My current assumptions for this question is that it is possible to run simple fluid dynamics in real-time (See Jos Stams implementation).