Artificial compressibility approaches in flux reconstruction for incompressible viscous flow simulations

Several competing artificial compressibility methods for the incompressible flow equations are examined using high-order flux reconstruction method. The established method (ACM) of \citet{Chorin1967} is compared to alternative entropically damped (EDAC) \citet{Clausen2013}, as well an ACM formulation with hyperbolised diffusion. While former requires solution be converged a divergence free state at each physical time step through pseudo iterations, latter can applied explicitly. We examine sensitivity both parameterisation series test cases over range Reynolds numbers. As reduced, EDAC found give linear improvements in whereas yields diminishing returns. For Taylor--Green vortex, perform well; however on more challenging circular cylinder $Re=3900$, gives rise early transition shear-layer and over-production turbulence kinetic energy. This attributed spatial pressure fluctuations Similar behaviour observed aerofoil $Re=60,000$ attached transitional boundary layer. It concluded that hyperbolic diffusion beneficial but cost case setup time, efficient flow. However, care must taken have significant impact physics remedy causes governing equation become overly stiff.