The Kinked String Was Fine, the Cut String Overshot by 9% — How the 1747 Wave-Equation Fight Ended Numerically
·5 min read
d'Alembert's travelling waves and Bernoulli's sine series are the same solution, until you truncate. Code shows where the 9% overshoot comes from and why smoothness decides.
The Outlet Is Open, Yet the Wave Comes Back — NSCBC and the Price of σ
·8 min read
At a non-reflecting outlet, one coefficient sets both reflection and pressure drift
Supersonic Flow Can't See Upstream — Characteristics and Sound Waves in the Euler Equations
·5 min read
Why a small disturbance splits into three characteristic speeds
When Characteristics Collide, a Shock Is Born — Burgers and the (x,t) Plane
·5 min read
How nonlinear self-advection breaks a smooth curve into a shock.