Journal of Scientific Computing

, Volume 79, Issue 2, pp 1015–1056 | Cite as

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

  • Juntao HuangEmail author
  • Weifeng Zhao
  • Chi-Wang Shu


In this paper, we extend our previous work in Huang and Shu (J Sci Comput, 2018. 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.


Compressible Euler equations Positivity-preserving Chemical reactions Production–destruction equations Finite difference Third-order accuracy 



We would like to thank Xiangxiong Zhang from Purdue University for many fruitful discussions.


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Authors and Affiliations

  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA
  2. 2.Department of Applied MathematicsUniversity of Science and Technology BeijingBeijingChina
  3. 3.Division of Applied MathematicsBrown UniversityProvidenceUSA

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