Implementing multi-directional molecular diffusion terms into Reaction Diffusion Manifolds (REDIMs)

Abstract The Reaction Diffusion Manifold (REDIM) method requires specifying an estimate of the system’s gradients as an input to characterize the molecular transport effects. So far, applications used a gradient estimate taken from simple combustion scenarios, like one-dimensional flame simulations. However, because the reduced model is typically used in turbulent combustion simulations, gradient estimates from a representative turbulent combustion scenario appear more appropriate. In this work, we study how gradients from Direct Numerical Simulations (DNS) of a turbulent flame can be incorporated into the REDIM method. A method for analyzing scalar gradients from a DNS simulation, and for representing them in a form that is usable in the REDIM method, is presented and applied. The analysis reveals a hierarchical structure in the local gradient directions of different scalars, which enables construction of gradient estimates on different levels of complexity (and fidelity). It is shown how these different levels appear in the dissipation terms of the REDIM equation. The influence of varying the detail of the DNS-based gradient estimate is studied, and it is found that the addition of the more complex levels has minor influence only on the REDIM. It can have an influence, however, onto the dynamics of the combustion system on the REDIM, i.e., onto the trajectory that the system takes on the REDIM.