Appendix D: Why Not Digital Waveguides?

Classic digital waveguides (Smith, 1992) model linear wave propagation with constant impedance \(Z_0 = \rho c / A\). They are computationally cheap but have severe limitations for engine exhaust:

• No nonlinear steepening: cannot produce shock waves – essential for the percussive “crack” of a high‑pressure blowdown.
• Constant speed of sound: temperature‑dependent \(c\) is ignored, leading to incorrect tuning of resonances when exhaust gas is hot.
• No mean flow advection: Doppler shift and flow‑induced damping are absent.
• No variable density or temperature: coupling with 0‑D thermodynamic volumes is inconsistent because the waveguide does not track mass or energy.

Our staggered‑grid PHS approach solves the full Euler equations on the same spatial grid, capturing all these effects while retaining real‑time performance via the implicit solver. No hybrid compromise is necessary.