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

MSC:
35Q31 Euler equations
76V05 Reaction effects in flows
76M20 Finite difference methods applied to problems in fluid mechanics
Software:
RODAS
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References:
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