An observable regularization of reactive compressible flows

A common feature of many flows involving shocks, turbulence and two-phase flows are the development of a continuous generation of small scales what we identified in the past as $k_\infty$ irregularity. We have recently introduced the concept of observable field quantities, which resulted in the derivation of an observable divergence theorem and eventually the observable Euler and Navier-Stokes equations in order to address the $k_\infty$ irregularity. We have had some promising results in the past simulating flows with shocks, turbulence, and two-phases using observable equations. In this talk we will extend the application of the observable equations to multispecies reactive flow problems. In particular, we present result from simulations of canonical one-dimensional over-driven detonation and deflagration problems. The results of observable simulations will be contrasted against analytical solutions, i.e. ZND solution, and available computations from the literature. All observable simulations are performed using a pseudo-spectral method in order to avoid any contamination of the simulations with numerical dissipation.