Compare different discretization schemes used in CFD (upwind, central, QUICK).

Discretization schemes approximate convective terms in transport equations. First-order upwind: uses upstream cell value, unconditionally stable but introduces numerical diffusion that smears gradients, order O(Δx). Central differencing: uses average of neighboring cells, second-order accurate O(Δx²) but can produce unbounded oscillations (wiggles) when Peclet number Pe = ρVΔx/Γ > 2. Second-order upwind: quadratic interpolation using two upstream cells, reduces numerical diffusion, O(Δx²). QUICK (Quadratic Upstream Interpolation): third-order scheme using quadratic profile through two upstream and one downstream cell, O(Δx³), good balance of accuracy and stability. TVD schemes (Total Variation Diminishing) with flux limiters combine accuracy in smooth regions with stability near discontinuities. Selection based on flow physics, mesh quality, and accuracy requirements.