Positivity-Preserving Time Discretizations for Production–Destruction Equations with Applications to Non-equilibrium Flows

  • Juntao HuangEmail author
  • Chi-Wang Shu


In this paper, we construct a family of modified Patankar Runge–Kutta methods, which is conservative and unconditionally positivity-preserving, for production–destruction equations, and derive necessary and sufficient conditions to obtain second-order accuracy. This ordinary differential equation solver is then extended to solve a class of semi-discrete schemes for PDEs. Combining this time integration method with the positivity-preserving finite difference weighted essentially non-oscillatory (WENO) schemes, we successfully obtain a positivity-preserving WENO scheme for non-equilibrium flows. Various numerical tests are reported to demonstrate the effectiveness of the methods.


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



We would like to thank Xiangxiong Zhang from Purdue University and Tao Xiong from Xiamen University for many fruitful discussions.


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Authors and Affiliations

  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA
  2. 2.Division of Applied MathematicsBrown UniversityProvidenceUSA

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