A variational inequality formulation for transonic compressible steady potential flows: Radially symmetric transonic shock

摘要

We establish a variational inequality formulation that captures the transonicshock for a steady compressible potential flow. Its critical point satisfiesthe transonic equation; moreover the associated jump conditions across its freeboundary match the usual Rankine-Hugoniot jump conditions for a shock. By meansof example we validate our formulation, and establish the necessary andsufficient condition for the existence of a transonic shock. Numerical resultsare also discussed.