Viscous detonation in H₂‒O₂‒Ar using intrinsic low-dimensional manifolds and wavelet adaptive multilevel representation

Abstract

A standard ignition delay problem for a mixture of hydrogen-oxygen-argon in a shock tube is extended to the viscous regime and solved using the method of intrinsic low-dimensional manifolds (ILDM) coupled with a wavelet adaptive multilevel representation (WAMR) spatial discretization technique. An operator-splitting method is used to describe the reactions as a system of ordinary differential equations at each spatial point. The ILDM method is used to eliminate the stiffness associated with the chemistry by decoupling processes which evolve on fast and slow time scales. The fast time scale processes are systematically equilibrated, thereby reducing the dimension of the phase space required to describe the reactive system. The WAMR technique captures the detailed spatial structures automatically with a small number of basis functions thereby further reducing the number of variables required to describe the system. A maximum of only 300 collocation points and 15 scale levels yields results with striking resolution of fine-scale viscous and induction zones. Additionally, the resolution of physical diffusion processes minimizes the effects of potentially reaction-inducing artificial entropy layers associated with numerical diffusion.