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Journal of Scientific Computing
Published in: Journal of Scientific Computing 3/2019

11-10-2018

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

Authors: Juntao Huang, Chi-Wang Shu

Published in: Journal of Scientific Computing | Issue 3/2019

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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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Metadata
Title
Positivity-Preserving Time Discretizations for Production–Destruction Equations with Applications to Non-equilibrium Flows
Authors
Juntao Huang
Chi-Wang Shu
Publication date
11-10-2018
Publisher
Springer US
Published in
Journal of Scientific Computing / Issue 3/2019
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-018-0852-1

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