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

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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.

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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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Authors and Affiliations

  1. Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA

    Juntao Huang

  2. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    Chi-Wang Shu

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  1. Juntao Huang
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  2. Chi-Wang Shu
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Correspondence to Juntao Huang.

Additional information

Research supported by ARO Grant W911NF-15-1-0226 and NSF Grant DMS-1719410.

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Huang, J., Shu, CW. Positivity-Preserving Time Discretizations for Production–Destruction Equations with Applications to Non-equilibrium Flows. J Sci Comput 78, 1811–1839 (2019). https://doi.org/10.1007/s10915-018-0852-1

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  • DOI: https://doi.org/10.1007/s10915-018-0852-1

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