Simulations of diffusive, reactive, compressible flows with detailed chemistry using a high-order hybrid WENO-CD scheme

John Ziegler, California Institute of Technology

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Direct numerical simulations of two applications – irregular hydrocarbon detonation and spark ignition – have been conducted using the multicomponent, compressible, reactive Navier-Stokes equations in two spatial dimensions. The simulations utilize a hybrid, WENO/centered-difference numerical method, with low numerical dissipation, high-order shock capturing, and structured adaptive mesh refinement (SAMR). This enables the resolution of diffusive processes within reaction zones. For the first application, a minimally reduced chemistry and transport model for a propane-air mixture is used to accurately capture the induction time, chemical relaxation, and diffusive mixing within vortical structures evolving from the triple-point shear layers. For the second application, a reduced hydrogen-air model is used along with a no-slip boundary condition implemented through the use of the ghost fluid method. Our implementation includes new techniques for discontinuity flagging, scheme-switching, and high-order prolongation and restriction. In particular, the refined methodology does not require upwinded WENO at grid refinement interfaces for stability, allowing high-order prolongation and thereby eliminating a significant source of numerical diffusion within the overall code performance. Also, by using a Riemann problem-based shock detection, the coverage of the WENO scheme is precisely controlled. The method has been extensively tested with a series of one- and two-dimensional steady and unsteady verification tests, verifying the high-order accuracy of the diffusion terms and the convergence of the whole implementation in a SAMR framework.

Abstract Author(s): Jack Ziegler