ABSTRACT

A PDE that expresses the variation of ρ with x and t for a fluid, the equation of continuity,

∂ρ

∂t = ∇ · (vρ) (1.1)

states a basic physical principle, conservation of mass, where v fluid velocity vector ∇ divergence operator

∇ is a vector differential operator that has three components in specific coordinate systems, for example, see Table 1.1.