Continuity Equation

Time to brush up my math! Today is about the Navier-Stokes (N-S) equations, a set of differential equations describing the behavior of moving fluid. The continuity equation is:

ρ ( rho) is density. u, v, w, is velocity along direction x, y, z. For incompressible fluid density is constant (does not change over time or space), so the equation can be written as

or

means the divergence (∇) of vector field (velocity in this case) U equals zero (a scalar value). In other words: during the infinitesimal time, through the closed surface of the infinitesimal volume around a given point, inward flow equals outward flow. Anything flows in must flow out, nothing is created, so the mass of the system is preserved. This idea is the very backbone of fluid simulation.

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