Mass-Continuity

Anelastic mass continuity equation from Clark (1977), Eq. 2.4. The component forms the three density-weighted velocity components rho_u = ρ̄u, rho_v = ρ̄v, rho_w = ρ̄w from the base-state density ρ̄ and the velocity field (u, v, w), and computes the anelastic mass-continuity residual mass_continuity as the sum of the three externally-supplied density-weighted divergence terms ∂(ρ̄u)/∂x + ∂(ρ̄v)/∂y + ∂(ρ̄w)/∂z. The anelastic approximation constrains this residual to zero, filtering acoustic (sound) waves from the dynamics by replacing the geometric velocity divergence with the density-weighted one. Four purely-algebraic equations, no time integration. Migrated from AtmosphericDynamics.jl@816cc391 src/clark1977.jl:369 (`AnelasticMassContinuity` @component).