Computational Techniques for PDEs: Discretization and Stability Analysis

A: That's the most common mistake — confusing solver availability with verification intent. The difference matters because V&V 20 cares about whether global outputs like drag are grid-invariant, and without strict local conservation you can hit false convergence where residuals drop but forces keep moving.

A: That's the most common mistake — confusing steady-state intent with explicit stability. The difference matters because CFL is velocity times dt over cell size, so 30 × dt / 0.005 ≈ 1 gives dt around 1e-4 before anything blows up.

A: That's the most common mistake — confusing a mesh metric with a turbulence closure assumption. The difference matters because wall functions expect y+ in the log layer, and forcing y+ <1 there corrupts shear stress prediction.

A: That's the most common mistake — equating formal order with physical fidelity. The difference matters because hyperbolic systems propagate information along characteristics, and ignoring that near shocks gives you Gibbs-style ringing.