对流占优问题的非线性QUICK格式
A Nonlinear QUICK Scheme for Convection-Dominated Equations
DOI: 10.12677/AAM.2018.712193, PDF,    科研立项经费支持
作者: 周艳娇, 高 巍：内蒙古大学数学科学学院，内蒙古 呼和浩特
关键词: QUICK格式；有限体积法；间断阈值；QUICK Scheme； Finite Volume Method； Discontinuous Threshold
摘要: 本文构造了一种新的非线性加权格式，利用这种加权格式对对流项进行离散，在加权系数中构造了新的间断阈值来判断光滑与间断，使得此格式在间断的时候利用一阶迎风格式，这样可以避免振荡，而在光滑解部分用三阶QUICK格式保证了三阶精度，然后利用三阶Runge-Kutta方法对时间进行离散，进而保证整体精度，使得数值解达到比较好的逼近效果。
Abstract: This paper constructed a nonlinear weighted scheme. The convective term is discretized by this new nonlinear weighted scheme. A new discontinuous threshold in the weighted coefficient is constructed to judge the smoothness and discontinuity, so that the scheme uses the first-order upwind scheme near the discontinuity which the oscillation can be avoided, and the third-order QUICK scheme is used to ensure the third-order accuracy in the smooth region. Time discretization is fulfilled by using the third order Runge-Kutta scheme. The new scheme achieves optimal order accuracy. It makes the numerical solution achieve a better approximation effect.
文章引用：周艳娇, 高巍. 对流占优问题的非线性QUICK格式[J]. 应用数学进展, 2018, 7(12): 1650-1657. https://doi.org/10.12677/AAM.2018.712193

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