Transonic small disturbance calculations including entropy corrections

Murman's fully conservative mixed type finite-difference operators are first modified. A special sonic point operator with an iterative damping term is introduced which helps the convergence and does not affect the spatial conservative differences. Reliable calculations with second order supersonic schemes are obtained using two sonic operators, the regular sonic point operator followed by a first order supersonic scheme. Also, shock point operator is shown to be equivalent to fitting a locally normal shock terminating the supersonic region. The potential calculations are then modified to account for the non-isentropic jump conditions using a simple shock fitting procedure based on Prandtl relation. The entropy increase across the shock is calculated in terms of the Mach number upstream of the shock and the effect of the generated vorticity is estimated via Crocco relation. Different examples are calculated and extensions to the full potential equation are discussed.