Comparing the performance and accuracy of a pressure based and a density-based coupled solver

The velocity-pressure-density coupling algorithms that are at the core of computational fluid dynamics (CFD) methods can be grouped into two distinct groups: pressure-based and density-based methods. Pressure-based methods were originally developed for incompressible flows but have since been extended to address a wide range of flow conditions including compressible all speed flows. They are nowadays used in most commercial CFD codes both in their segregated and coupled form. Density-based methods, on the other hand, originated in the aeronautics industry for the simulation of compressible flows, and have thus been the dominant method used in the simulation of transonic and supersonic flows especially in aerodynamics applications. However, just as for pressure-based methods, a variety of techniques have over the years extended their ability to operate in low Mach and incompressible flow regimes. Turbomachinery applications is one area where competition between pressure-based and density-based solvers is still the norm in commercial, academic and open source codes, with both methods being used in diverse research groups and communities. While an extensive study would be required to clearly determine and evaluate the strength and weaknesses of these methods in this application area, the aim of this paper is to gain a better appreciation of the performance and accuracy of two state of the art codes, namely LINARS a density-based code developed at Graz University of Technology and coupledFoam, a pressure-based coupled solver developed on top of the OpenFOAM TM toolbox, noting that both solvers resolve the Navies Stokes equations in a coupled fashion.