Numerical Simulation of Shock-Turbulence Interactions Using High-Order Shock-Fitting Algorithms

Abstract

High-order methods are critical for reliable numerical simulation of strong-shock and turbulence interaction problems. Such problems are not well understood due to limitations of numerical methods. Most widely used shock capturing methods for the numerical simulation of compressible flows are inherently dissipative, only first order accurate and may incur numerical oscillations near the shock waves. In our previous work [1, 2] we have shown that algorithms based on shock-fitting methodology can solve the flow with highorder accuracy near as well as away from the shocks without any numerical oscillations. In the current study, we extend the fifth order shock-fitting algorithm to carry out Direct Numerical Simulations (DNS) of interactions of shock waves with realistic isotropic turbulence. Incoming isotropic turbulence is developed in a temporal simulation of solenoidal fluctuations in a periodic box. Using Taylor’s hypothesis these fluctuations are prescribed upstream of the shock wave and the flow behind the shock wave is computed using the shock fitting algorithm. In this paper we investigate interactions of isotropic turbulence with normal shock waves of Mach numbers 1 2.0 10.0