Direct numerical simulation of the interaction of isotropic turbulence with a shock wave using shock-fitting

The interaction of three-dimensional isotropic turbulence with a plane shock at Mach numbers of $M=2.0$ and $M=3.0$ is investigated via direct numerical simulation. The numerical scheme is based on a characteristic-type formulation of the Navier–Stokes equations and uses fifth-order upwind schemes in space, a fourth order Runge Kutta scheme in time and a shock-fitting as inlet condition. The isotropic turbulence was generated in a separate computation based on a prescribed energy spectrum. This turbulent flow is considered as frozen, and is convected through the shock with a prescribed average shock speed. An FFT interpolation is used to obtain the upstream values at the instantaneous shock location. Turbulence enhancement is observed, and the evolution of velocity fluctuations as well as turbulence microscales are in good agreement with the behaviour observed using shock-capturing. To cite this article: J. Sesterhenn et al., C. R. Mecanique 333 (2005).