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

  • Juntao Huang
  • Chi-Wang Shu
Article
  • 56 Downloads

Abstract

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.

Keywords

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

Notes

Acknowledgements

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

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

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

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