Novel method for Lagrangian-particle analysis of highly compressible reacting turbulence

Highly compressible turbulent reacting flows involve complex phenomena, such as non-linear turbulence-chemistry interactions, and deflagration-to-detonation transition. Lagrangian-particle tracking can provide a powerful analysis framework of the flow complementary to Eulerian based formulation. Accurate advection of massless Lagrangian fluid parcels in highly turbulent flows places stringent requirements on the integration algorithms in terms of numerical errors. We discuss the development of accurate integration and interpolation methods with particular focus on the flows with discontinuities or high gradients induced by shock waves or flame fronts. Under these conditions, traditional smooth interpolation schemes are inaccurate. This problem is solved by Weighted-Essentially-Non-Oscillatory-type (WENO) interpolation schemes. Also, we show that time integrators with symplectic properties ensure that trajectory errors remain bounded in time. The accuracy of these methods is verified and is then applied in direct numerical simulations (DNS) of fast, highly compressible, premixed turbulent reacting flows.