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Huang, Juntao; Zhao, Weifeng; Shu, Chi-Wang

A third-order unconditionally positivity-preserving scheme for production-destruction equations with applications to non-equilibrium flows. (English) Zbl 1444.35125

J. Sci. Comput. 79, No. 2, 1015-1056 (2019).
Summary: In this paper, we extend our previous work in [the first and the third author, ibid. 78, No. 3, 1811–1839 (2019; Zbl 1420.35190)] 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 [loc. cit.], 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.

Cited in 1 Review
Cited in 24 Documents

MSC:

35Q31 Euler equations
76V05 Reaction effects in flows
76M20 Finite difference methods applied to problems in fluid mechanics

Keywords:

compressible Euler equations; positivity-preserving; chemical reactions; production-destruction equations; finite difference; third-order accuracy

Citations:

Zbl 1420.35190

Software:

RODAS
Cite Review PDF
Full Text: DOI

References:

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