CFD

CFD solves the conservation laws: continuity ∂ρ/∂t + ∇·(ρV) = 0, the Navier-Stokes momentum equations, and energy. These coupled PDEs are discretised and solved numerically, per Versteeg & Malalasekera.

Discretisation converts PDEs to algebraic equations at grid points; the central-difference approximation ∂φ/∂x ≈ (φ_{i+1} − φ_{i−1})/(2Δx) is second-order accurate. FDM, FVM, and FEM are the main schemes, per Versteeg & Malalasekera.

Turbulence models close the Reynolds-averaged equations; the k-ε model solves transport equations for turbulent kinetic energy k and its dissipation ε. RANS, LES, and DNS trade cost against fidelity, per Versteeg & Malalasekera.

A grid-independence study refines the mesh until the solution stops changing, so results do not depend on grid resolution. The Grid Convergence Index GCI = F_s|ε|/(rᵖ − 1) quantifies discretisation uncertainty, per CFD best-practice (Roache).

Validation compares CFD predictions with experimental (or analytical) data: error = |CFD − experiment|/experiment × 100 %. It confirms the model represents reality, distinct from verification, per CFD best-practice.