A Variational Inequality Formulation for Transonic Compressible Steady Potential Flows: Radially Symmetric Transonic Shock

Abstract

We establish a variational inequality formulation that captures the transonic shock for a steady compressible potential flow. Its critical point satisfies the transonic equation; moreover the associated jump conditions across its free boundary match the usual Rankine--Hugoniot jump conditions for a shock. By means of example we validate our formulation and establish the necessary and sufficient condition for the existence of a transonic shock. Numerical results are also discussed.