Ideal-gas sound speed from pressure

Purpose

When static pressure and density are available, the isentropic sound speed is evaluated directly without going through total enthalpy.

Formula

\[c = \sqrt{\gamma\frac{p}{\rho}}\]

Relation to the total-enthalpy form

IdealGasSoundSpeed uses

\[c = \sqrt{(\gamma-1)\bigl(H-\tfrac12|u|^{2}\bigr)}\]

which is equivalent for a calorically perfect gas when (H=h+tfrac12|u|^{2}) and (h=gamma p/((gamma-1)rho)).

Source map

  • IdealGasSoundSpeedFromPressure in NsInvFluxPolicy

  • Related: IdealGasSoundSpeed, RoeAbsoluteEigenvalues

  • Tests: tests/solver/inv_flux_policy_test.cpp

  • Theory table: tools/verification/data/ideal_gas_sound_speed_from_pressure_theory.csv

  • Contract Workbench id: ideal_gas_sound_speed_from_pressure

Sound speed vs pressure

What this proves / does not prove

Proves: (c=sqrt{gamma p/rho}) matches the pure API on a pressure grid.

Does not prove: numerical identity with the total-enthalpy form on every Roe-averaged state (separate consistency tests).

References