An adaptive high-order hybrid scheme for compressive, viscous flows with detailed chemistry

Abstract

A hybrid weighted essentially non-oscillatory (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. The method enables accurate resolution of diffusive processes within reaction zones. The approach combines time-split reactive source terms with a high-order, shock-capturing scheme specifically designed for diffusive flows. A description of the orderoptimized, 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 new techniques for discontinuity flagging, scheme-switching, and high-order prolongation and restriction is described. 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. A series of oneand two-dimensional test problems is used to verify the implementation, specifically the high-order accuracy of the diffusion terms. One-dimensional benchmarks include a viscous shock wave and a laminar flame. In two space dimensions, a Lamb-Oseen vortex and an unstable diffusive detonation are considered, for which quantitative convergence is demonstrated. Further, a two-dimensional high-resolution simulation of a reactive Mach reflection phenomenon with diffusive multi-species mixing is presented.

Adaptive simulations of viscous detonations initiated by a hot jet using a high-order hybrid WENO–CD scheme

“…In comparison, in Fig.4(b) irregular small-scale vortices are clearly visible both along the shear layer and underneath the upper wall. The results in Fig.4(b) are different from those in [17] where Euler equations are solved with a MUSCL-TVD scheme, which is due to the absence of not only physical viscosity in Euler equations but also numerical dissipation involved in the hybrid WENO-CD scheme. Compared with Fig.4(b) a more regular structure of the large-scale vortices can be observed in Fig.4(a).…”

“…Here, the simplified chemistry model is selected and fitted to physical parameters of a H2/O2 detonation. The details of the governing equations and the thermodynamic parameters of the chemistry model can be found in [17], while the reaction model is discussed in depth in [26]. At the end of the ZND reaction zone, the temperature is about 2500 K and the pressure is about …”

Dynamical separation of spherical bodies in supersonic flow

“…Numerical approach As in Laurence & Deiterding (2011), we employ the Cartesian fluid solver framework AMROC (Deiterding 2005b;Deiterding et al 2005Deiterding et al , 2007Deiterding 2009Deiterding , 2011aZiegler et al 2011) to simulate numerically the fluid-structure interaction of the free-flying spherical bodies. The equations solved to model the inviscid compressible fluid are the Euler equations in conservation-law form…”

Numerical Investigation on Detonation Control Using a Pulse Hot Jet in Supersonic Combustible Mixture

“…Based on these ideas above, we conducted a series of numerical simulations on detonation initiation and propagation using a hot jet in supersonic combustible mixtures (Cai et al, 2015a;Liang et al, 2014;Cai et al, 2014;Cai et al, 2015b;Cai et al, 2016a;Cai et al, 2016b) with the open-source program AMROC (Deiterding, 2003;Liang et al, 2007;Deiterding, 2009;Deiterding, 2011;Ziegler et al, 2011) …”