fluidsim/algorithm_description.txt at master · quinor/fluidsim · GitHub

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THE MODEL


parameters:

I - inertia, 0.9
A - acceleration, 5


edge parameters
    V_ij - velocity (desired flow per tick) between node i and j
        V_ij = -V_ji
    F_ij - actual flow in current tick


node parameters
    basic
        C_i - capacity
        T_i - current volume
        P_i - pressure (like in current system)
    auxiliary (computed for the needs of the algorithm)
        Vin_i, Vout_i - summaric in/out velocities of a node
        Sin_i, Sout_i - satisfaction for incoming and outcoming flow (what fraction of Vin/Vout can be satisfied)


in each tick:
    # update the velocities
    for each connection i, j:
        V_ij := V_ij * I + sgn(P_j-P_i) * A

    # compute auxiliary values
    for each i:
        Vin_i = sum_j max(0, V_ji)
        Vout_i = sum_j max(0, V_ij)

        Sin_i = min(Vin_i, C_i-T_i) / Vin_i
        Sout_i = min(Vout_i, T_i) / Vout_i

    # apply flow
    for each connection i, j such that Fij > 0:
        V_ij := min(Sout_i, Sin_j) * V_ij
        T_i -= V_ij
        T_j += V_ij

    # handle other stuff, ie. pumps or fluid-handling machines