Mach-uniformity through the coupled pressure and temperature correction algorithm

We present a new type of algorithm: the coupled pressure and temperature correction algorithm. It is situated in between the fully coupled and the fully segregated approach, and is constructed such that Mach-uniform accuracy and efficiency are obtained. The essential idea is the separation of the convective and the acoustic/thermodynamic phenomena: a convective predictor is followed by an acoustic/thermodynamic corrector. For a general case, the corrector consists of a coupled solution of the energy and the continuity equations for both pressure and temperature corrections. For the special case of an adiabatic perfect gas flow, the algorithm reduces to a fully segregated method, with a pressure-correction equation based on the energy equation. Various test cases are considered, which confirm that Mach-uniformity is obtained.