🏃 Inertia
The left side describes how a parcel of air accelerates locally and as it moves through spatial velocity gradients.
Navier–Stokes Principles for Structural Wind Engineering
The Navier–Stokes equations express conservation of momentum for a moving fluid. In structural wind engineering, they connect the approaching atmosphere to velocity, pressure, turbulence and ultimately structural loading.
ρ(∂u/∂t + (u·∇)u) = −∇p + μ∇²u + ρg
📉 Pressure
−∇p drives and redirects flow. Pressure integrated over a surface becomes the force transferred to a structure.
🫧 Viscosity
μ∇²u represents momentum diffusion due to viscosity. In high-Reynolds-number wind, turbulence modeling becomes especially important.
🌬️ Why structural engineers care
Wind approaching a building, bridge or roof separates at corners, accelerates around geometry and forms wakes. CFD numerically approximates these governing equations over a mesh. Surface pressures can then be integrated into forces and moments, while unsteady pressures can drive vibration and fatigue.
Atmospheric wind→Navier–Stokes / CFD→Surface pressure→Forces & moments→Structural response
🧮 Incompressible continuity
∇ · u = 0
For many building-wind applications at ordinary wind speeds, air is treated as approximately incompressible. The continuity equation requires mass conservation through the flow field.
⚠️ What these equations do not remove
Solving the equations numerically does not automatically make a model valid. Domain size, mesh resolution, wall treatment, inlet turbulence, turbulence model, time step, convergence, sampling duration, terrain representation and validation all affect whether the output is suitable for engineering use.