High-order hybrid scheme for compressive, viscous flows with detailed chemistry

John Ziegler, California Institute of Technology

A hybrid WENO/centered-difference numerical method, with low numerical dissipation, high order shock-capturing, and structured adaptive mesh refinement (SAMR), has been developed for the direct numerical simulation of the multicomponent, compressive, reactive Navier-Stokes equations. Diffusive processes within the reaction zones are resolved. The method combines time-split reactive source terms with a high order (ignoring 1st order errors at shocks) shock capturing scheme specifically designed for diffusive flows. A description of the order-optimized, symmetric, finite-difference, flux-based, hybrid WENO/centered-difference scheme is given, along with its implementation in a high-order SAMR framework. The implementation of the discontinuity flagging, scheme-switching, and high-order prolongation and restriction is described. A series of one- and two-dimensional problems is used to verify the implementation, specifically the high-order accuracy of the diffusion terms. This has led to the simulation of reactive Mach reflection phenomena with diffusive multi-species mixing. These results, supported by verification problems, are presented for a viscous shock wave, decaying Lamb-Oseen Vortex, Viscous DMR, laminar flame, and spark ignition.

Abstract Author(s): John Ziegler