Fire: An open-source adaptive mesh refinement solver for supersonic reacting flows

In this study, we introduce Fire, an open-source adaptive mesh refinement (AMR) solver for supersonic reacting flows, and conduct theoretical analyses on the efficiency of AMR methods. Fire is developed within the AMR framework of ECOGEN (Schmidmayer et al., 2020). To accurately model compressible multi-component reacting flows, the Fire solver employs the thermally perfect gas model for multi-species gaseous mixtures, mixture-averaged transport models for viscous fluxes, and detailed finite-rate chemistry for combustion processes. The solver utilizes the Harten-Lax-van Leer Contact approximate Riemann solver with low-Mach number correction to evaluate inviscid fluxes, demonstrating its superiority over the traditional Harten-Lax-van Leer Contact solver on detonation simulations. Moreover, we deduce the theoretical speedup ratio (denoted as ${\eta }_{\text{the}}$) of AMR methods over uniform-grid methods by analyzing the advancing procedures. This theoretical analysis is well-supported by the numerical speedup ratio (denoted as ${\eta }_{\text{num}}$) given by numerical tests. To further enhance computational efficiency, we propose a three-stage AMR strategy specifically tailored to the characteristics of inert flows, flame fronts, and shock-flame interactions. Comprehensive validation tests, encompassing unsteady convection and diffusion, planar deflagration, inert and reacting shock-bubble interactions, planar detonations, and detonation cellular structures, confirm the accuracy and efficiency of Fire in simulating supersonic combustions. We anticipate that this work will not only serve as a valuable numerical tool for supersonic reacting flows research but also contribute to a deeper understanding and improvement of AMR methodologies.