The numerical simulation of time-dependent flames with realistic physical models presents a number of technical challenges. In particular, the tight coupling between fluid dynamics and combustion thermochemistry ensures that spurious numerical diffusion and/or under-resolution of the flow field will lead to inaccurate prediction of flame characteristics, while extremely short chemical time scales may make many standard time integration algorithms impractical on all but the largest computing clusters. In this work, we present a new numerical method that aims to address both of these challenges through the use of high order compact finite difference schemes and a robust, fully implicit, Newton-Krylov solver. After discussing the algorithms behind the "implicit-compact" approach and some challenges of their implementation, we compare the performance of the method to that of a conventional low order Newton-based flame code on several oscillating axisymmetric laminar diffusion flames with one-step chemistry. Calculations of forced flames over a range of forcing levels permit a quantitative assessment of the improvement offered by the high order method, while simulations of unforced, flickering flames underline the benefits of high resolution numerical schemes for the study of unstable or sensitive phenomena in combustion.
展开▼
