In this study, a family of second-order process based modified Patankar Runge-Kutta schemes is proposed. The proposed schemes preserve both the mass and mole balance in a stiff reaction network while maintaining the positivity of density and pressure. The accuracy analysis is conducted to derive the sufficient and necessary conditions for the Runge-Kutta and Patankar coefficients. Coupling with the finite volume method, the proposed schemes are extended to Euler equations with non-equilibrium reacting source terms. Benchmark tests are given to prove the prior order of accuracy and validate the positive-preserving property for both density and pressure.

在这项研究中，提出了一系列基于二阶过程的改进的Patankar Runge-Kutta方案。所提出的方案在保持刚性反应网络的同时保持质量和摩尔平衡，同时保持密度和压力的正值。进行精度分析以得出Runge-Kutta和Patankar系数的充分必要条件。结合有限体积方法，将所提方案扩展到具有非平衡反应源项的欧拉方程。进行基准测试以证明准确性的先后顺序，并验证密度和压力的正保性。