A Third-Order Unconditionally Positivity-Preserving Scheme for Production-Destruction Equations with Applications to Non-equilibrium Flows

In this paper, we extend our previous work in Huang and Shu (J Sci Comput, 2018. 10.1007/s10915-018-0852-1) and develop a third-order unconditionally positivity-preserving modified Patankar Runge-Kutta method for production-destruction equations. The necessary and sufficient conditions for the method to be of third-order accuracy are derived. With the same approach as Huang and Shu (2018), this time integration method is then generalized to solve a class of ODEs arising from semi-discrete schemes for PDEs and coupled with the positivity-preserving finite difference weighted essentially non-oscillatory schemes for non-equilibrium flows. Numerical experiments are provided to demonstrate the performance of our proposed scheme.