A Third-Order Unconditionally Positivity-Preserving Scheme for Production–Destruction Equations with Applications to Non-equilibrium Flows
A Third-Order Unconditionally Positivity-Preserving Scheme for Production–Destruction Equations with Applications to Non-equilibrium Flows
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DOI：
10.1007/s10915-018-0881-9
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发表时间：
2018-11
影响因子：
2.5
通讯作者：
Juntao Huang;Weifeng Zhao;C. Shu
中科院分区：
文献类型：
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作者：
Juntao Huang;Weifeng Zhao;C. Shu
在本文中，我们在Huang和Shu （J Sci computer, 2018）中扩展了我们之前的工作。https://doi.org/10.1007/s10915-018-0852-1)，建立了生产-破坏方程的三阶无条件保正修正Patankar龙格-库塔方法。给出了该方法具有三阶精度的充分必要条件。采用与Huang和Shu（2018）相同的方法，然后将该时间积分方法推广到求解一类由偏微分方程的半离散格式产生的偏微分方程，并与非平衡流的保正有限差分加权基本非振荡格式相结合。数值实验验证了所提方案的性能。
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.