Tabulated chemistry for detonations in a spatially-filtered framework*

Recently, we have developed a spatially-filtered framework for simulating shock-dominated flows which introduced sub-filter scale terms to regularize the governing equations. For detonations, the filtered shock thickness is assumed to be at least an order of magnitude smaller than the induction length, and the mixture composition is not affected by the filtering. To reduce the cost of simulations, the chemistry can be simplified through tabulation. The chemical evolution is reduced to the solution of a progress variable transport equation, which is then used to look up relevant thermochemical quantities in a pre-computed table. Of particular importance is the source term, which describes the rate at which chemical reactions are occurring. If the filtered shock thickness approaches the induction length, the filtering of the chemical reaction zone must also be considered. In this work, the effect of filtering the source term is studied in detail. The source term is filtered a priori and tabulated for a range of filter widths. The tables are then used in simulations with varying grid resolutions. The combined effect of filter width and grid resolution on relevant physical parameters such as the detonation velocity are presented.