Positivity-Preserving Time Discretizations for Production–Destruction Equations with Applications to Non-equilibrium Flows
Positivity-Preserving Time Discretizations for Production–Destruction Equations with Applications to Non-equilibrium Flows
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DOI：
10.1007/s10915-018-0852-1
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发表时间：
2018-10
影响因子：
2.5
通讯作者：
Juntao Huang;Chi-Wang Shu
中科院分区：
文献类型：
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作者：
Juntao Huang;Chi-Wang Shu
本文对生产-破坏方程构造了一族修正的Patankar Runge-Kutta方法，该方法是保守的且无条件保正的，并得到了获得二阶精度的充要条件.这个常微分方程求解器，然后扩展到解决一类半离散格式的偏微分方程。将这种时间积分方法与保正加权基本无振荡（韦诺）格式相结合，成功地得到了一种求解非平衡流的保正韦诺格式.各种数值试验报告，以证明该方法的有效性。
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.