Improvements and Extensions to a Full-Potential Formulation Based on Independent Fields

The paper presents a full-potential model for nonisentropic unsteady transonic flows extending a parent formulation based on an independent approximation of the density and velocity potential fields. It retains the advantage of the existence of a velocity potential while granting a unique solution by combining a correction of the stagnation pressure behind a shock with a new form of Kutta condition. The solution procedure relies on an unstructured, node-based, finite volume approximation, with linear shape functions and nonreflecting far-field boundary conditions. An improved upwind density biasing allows the solution in supersonic regions to be stabilized. A new proof is given for the linearized unconditional stability of the implicit solver adopted for subsupersonic asymptotic conditions. Numerical results show that the method can model Euler solutions more accurately than an isentropic full-potential formulation, for both steady and unsteady conditions. Applications to asymptotically supersonic flows complete the numerical validation.