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 . https://doi.org/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 condit...

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Published in:Journal of scientific computing Vol. 79; no. 2; pp. 1015 - 1056
Main Authors: Huang, Juntao, Zhao, Weifeng, Shu, Chi-Wang
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2019
Springer Nature B.V
Subjects:
Algorithms
Chemical reactions
Computational Mathematics and Numerical Analysis
Equilibrium
Essentially non-oscillatory schemes
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Nonequilibrium flow
Numerical analysis
Runge-Kutta method
Theoretical
Time integration
Production–destruction equations
Finite difference
Chemical reactions
Positivity-preserving
Compressible Euler equations
Third-order accuracy
ISSN:0885-7474, 1573-7691
Online Access:Get full text
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Summary:In this paper, we extend our previous work in Huang and Shu (J Sci Comput, 2018 . https://doi.org/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.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-018-0881-9