In this study, a temporally-evolving incompressible and compressible Turbulent Shear Layer (TSL) instability problem is solved using an all-speed (all-Mach), implicit, nondissipative and kinetic energy conserving algorithm. An in-house, fully parallel, finitevolume Direct Numerical Simulation (DNS) solver was developed using PETSc. Convergence characteristics at low-Mach numbers were also improved using a relaxation procedure. We aim here to assess the performance and behavior of the present algorithm for complex flows which contain multi-scale physics and gradually evolve into turbulence. The results show that the algorithm is able to produce correct physical mechanisms and capture the evolution of the turbulent fluctuations for both incompressible and compressible cases. It is observed that the non-dissipative and kinetic energy conserving properties make the algorithm powerful and applicable to challenging problems. For higher Mach numbers, a shock-capturing or a dissipative mechanism is required for robustness.

I. YILMAZ, F. O. EDIS, H. SAYGIN and L. DAVIDSON, “Parallel implicit DNS of temporally-evolving turbulent shear layer instability“, Journal of Computational amd Apllied Mathematics, Vol. 259, pp. 651-659 (2014).