prandtl-meyerlisted

# Prandtl-Meyer Expansion (aerodynamics/high-speed/prandtl-meyer) Use when the task is the Prandtl-Meyer expansion of a supersonic flow: the expansion angle from the Mach number, the downstream Mach number after the flow turns away from itself, the total turning angle of the fan, and the static pressure ratio across it. ## Domain quick reference - Prandtl-Meyer function: nu(M) = sqrt((gamma+1)/(gamma-1)) * atan(sqrt((gamma-1)/(gamma+1) * (M^2 - 1))) - atan(sqrt(M^2 - 1)), in radians. nu(1.0) = 0.0 exactly: the expansion fan collapses to zero width at the sonic point and widens monotonically above it. The function is undefined for subsonic Mach numbers (M < 1 raises ValueError). - Specific heat ratio: gamma (default 1.4 for air) must be > 1. - Total turning angle of an expansion fan: delta = nu(M2) - nu(M1) in radians for a flow turning away from itself; positive for an expansion (M2 > M1), negative for a compression (not a Prandtl-Meyer fan). - Downstream Mach after a turn: solve nu(M2) = nu(M1) + delta for M2, where delta is the turning angle in radians. Bisection on the bracket [1, 50] is deterministic and offline; a turning angle too large for the bracket raises ValueError. - Static pressure ratio: p2/p1 = pr(M2) / pr(M1) with the isentropic relation pr(M) = (1 + (gamma-1)/2 * M^2)^(-gamma/(gamma-1)); always < 1 for M2 > M1 (the expansion drops static pressure as it accelerates the flow). - Textbook anchor (Anderson, Modern Compressible Flow,