Analysis of shock relations for steady potential flow models

Potential flow models remain to be practically relevant, for both physical and numerical reasons. Detailed knowledge of their difference with rotational and viscous flow models is still important. In the present paper, this knowledge is reviewed and extended. Normal and oblique shock relations for the steady full potential equation and steady transonic small disturbance equation are derived. Among others, the deficiencies in conservation of mass and momentum across shock waves are analyzed in detail for these potential flow models. By comparison with the shock relations for the Euler equations guidelines are offered for the applicability of potential flow models in numerical simulations. Furthermore, the analytical expressions derived here may serve for verification of numerical methods.