🧠 PHYSICS PRIMER

Navier–Stokes Principles

The Navier–Stokes equations express conservation of momentum for fluids. Together with mass conservation, they describe how pressure, inertia, viscosity and external forces shape fluid motion.

🌊 Momentum equation

ρ(∂u/∂t + u·∇u) = −∇p + μ∇²u + ρg

ρ ∂u/∂tLocal acceleration

ρ(u·∇)uConvective inertia

−∇pPressure-gradient force

μ∇²uViscous momentum diffusion

ρgBody forces such as gravity

⚖️ Mass conservation

∇·u = 0 (incompressible flow)

For a constant-density incompressible fluid, velocity must satisfy continuity: fluid cannot disappear or appear inside the domain.

🔢 Why Reynolds number matters

Re = ρVL / μ

Reynolds number compares inertial effects with viscous effects. It helps identify whether viscosity dominates, transition matters, or turbulent behavior is likely to require a turbulence model or resolved transient simulation.

🧭 From equations to useful CFD

Geometry→Fluid properties→Boundary conditions→Discretization→Pressure + velocity fields→Domain decisions

🛡️ Numerical solution is not automatic validity

A solver can converge to a numerically consistent answer that is still unsuitable for a real decision. Mesh resolution, domain size, wall treatment, inlet profiles, turbulence modeling, time step, conservation, averaging, measurement comparison and uncertainty all matter.

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