A component-splitting implicit time integration for multicomponent reacting flows simulations

Abstract

A component-splitting method is proposed to improve the convergence characteristics of the implicit time integration for compressible multicomponent reactive flows. The characteristic decomposition of the flux Jacobian in multicomponent Navier–Stokes equations yields a large sparse eigensystem, presenting challenges of slow convergence and high computational cost for the implicit methods. To address this issue, the component-splitting method splits the implicit operator into two parts: one for the flow equations (density, momentum, and energy) and the other for the component equations. The implicit operators of each part employ flux-vector splitting with their respective spectral radii to achieve convergence acceleration. This approach avoids the exponential increase in computational time with the number of species and allows the implicit method to be used in multicomponent flows with a large number of species. Two consistency corrections are developed with the objective of reducing the component-splitting error and ensuring numerical consistency in mass fraction. Importantly, the impact of the component-splitting method on accuracy is minimal as the residual approaches convergence. The accuracy, efficiency, and robustness of the component-splitting method are extensively investigated and compared with the coupled implicit scheme through several numerical cases involving thermo-chemical nonequilibrium hypersonic flows. The results demonstrate that the component-splitting method reduces the number of iteration steps required for the convergence of residual and wall heat flux, decreases the computation time per iteration step, and diminishes the residual to a lower magnitude. The acceleration efficiency is enhanced with an increase in the Courant–Friedrichs–Lewy number and the number of species.