A midpoint-rule-based extrapolation solver for combustion CFD

Increasingly large chemical mechanisms are needed to predict autoignition, heat release and pollutant emissions in computational fluid dynamics (CFD) simulations of in-cylinder processes in compression-ignition engines and other applications. Calculation of chemical source terms usually dominates the computational effort, and several strategies have been proposed to reduce the high computational cost associated with realistic chemistry in CFD. Central to most strategies is a stiff ordinary differential equation (ODE) solver to compute the change in composition due to chemical reactions over a computational time step. Most work to date on stiff ODE solvers for computational combustion has focused on backward differential formula (BDF) methods, and has not explicitly considered the implications of how the stiff ODE solver couples with the CFD algorithm. Recently, advantages of extrapolation-based stiff ODE solvers have been demonstrated. In this work, improvements to extrapolation-based solvers with respect to accuracy and speedup are discussed. Benefits of applying the midpoint method in the extrapolation process as used in SIBS, instead of the Euler method as used in SEULEX, are shown. Implementation differences from the original SIBS implementation and how to improve it are discussed. The potential benefits of hybrid explicit/implicit integration are demonstrated. Benefits in CPU time and accuracy are shown for homogeneous systems and compression-ignition engines.