Novel lagrangian-particle tracking method for highly compressible, turbulent, reacting flows

In this paper, we discuss a novel Lagrangian-particle tracking method for highly compressible turbulent reacting flows. Both time integration and interpolation schemes are developed with the goal of providing high solution accuracy in the presence of discontinuities in the flow field created by shock waves or flame fronts. It is demonstrated that symplectic time integrators maintain the Lagrangian fluid parcel’s radial position errors low and bounded over the long-time integration periods. While phase errors can grow indefinitely with time, it is shown that they also remain low. Furthermore, it is demonstrated that once discontinuous flow fields are introduced, centered interpolation schemes do not provide adequate accuracy. In order to solve this problem, a new interpolation scheme is developed based on Weighted-Essentially-Non-Oscillatory (WENO) method. When temporal discretization errors are sufficiently small, the new WENO scheme can reduce the trajectory and phase errors by more than an order of magnitude in comparison with the traditional centered schemes. Presented approach can serve as the basis for high-fidelity, efficient numerical particle solvers for direct numerical and large-eddy simulations of high-speed, multiphase, compressible turbulent reacting flows found in hypersonic and detonation-based propulsion systems.