In this paper we present a fully coupled algorithm for the resolution of compressible flows at all speed. The pressure-velocity coupling at the heart of the Navier Stokes equations is accomplished by deriving a pressure equation in similar fashion to what is done in the segregated SIMPLE algorithm except that the influence of the velocity fields is treated implicitly. In a similar way, the assembly of the momentum equations is modified to treat the pressure gradient implicitly. The resulting extended system of equations, now formed of matrix coefficients that couples the momentum and pressure equations, is solved using an algebraic multigrid solver.

The performance of the coupled approach and the improved efficiency of the novel developed code was validated comparing results with experimental and numerical data available from reference literature test cases as well as with segregated solver as exemplified by the SIMPLE algorithm. Moreover the reference geometries considered in the validation process cover the typical aerodynamics applications in gas turbine analysis and design, considering Euler to turbulent flow problems and clearly indicating the substantial improvements in terms of computational cost and robustness.

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