On the Dynamics of Computing a Chemically Relaxed Nonequilibrium Flow

Abstract

In order to gain insights into the strong dependence of numerical solutions on initial data for finite time steps, a set of nonlinear test problems rich enough to capture the behavior of difference schemes were recently identified and the numerical basins of attraction for these problems were computed using commonly used time discretizations in CFD. Our study revealed a wealth of surprisingly nonlinear behavior of numerical schemes that were not observed before, in particular for the implicit time discretizations that are commonly used in CFD. The goal of this work is to apply these tools to study a practical model from non-equilibrium flowfield relaxation. This type of problem arises in chemically nonequilibrium hypersonic flows such as in a shock tube experiment or an expanding nozzle. Here we consider a reacting mixture of (N2, N) for an inviscid one-dimensional steady model. Preliminary numerical results indicate that, aside from the possibility of spurious numerical solutions being introduced by the time discretizations, limitations on the model for physical or accurate solutions may also play a part in the dynamics observed.