An in-depth study on the implementation aspect of unified time integrators in reactive two-phase flows with consistent time level

Purpose: A consistent implementation of the general computational framework of unified second-order time accurate integrators via the well-known GSSSS framework in conjunction with the traditional Finite Difference Method is presented to improve the numerical simulations of reactive two-phase flows. Design/methodology/approach: In the present paper, the phase interaction evaluation in the present implementation of the reactive two-phase flows has been derived and implemented to preserve the consistency of the correct time level evaluation during the time integration process for solving the two phase flow dynamics with reactions. Findings: Numerical examples, including the classical Sod shock tube problem and a reactive two-phase flow problem, are exploited to validate the proposed time integration framework and families of algorithms consistently to second order in time accuracy; this is in contrast to the traditional practices which only seem to obtain first-order time accuracy because of the inconsistent time level implementation with respect to the interaction of two phases. The comparisons with the traditional implementation and the advantages of the proposed implementation are given in terms of the improved numerical accuracy in time. The proposed approaches provide a correct numerical simulation implementation to the reactive two-phase flows and can obtain better numerical stability and computational features. Originality/value: The new algorithmic framework and the consistent time level evaluation extended with the GS4 family encompasses a multitude of past and new schemes and offers a general purpose and unified implementation for fluid dynamics.