论文标题
快速方案是具有点值数值解决方案的三阶有限体积方案
The QUICK Scheme is a Third-Order Finite-Volume Scheme with Point-Valued Numerical Solutions
论文作者
论文摘要
在本文中，我们解决了快速方案中永远存在的混乱：它是二阶方案或三阶方案。正如原始参考文献中提出的快速方案[B. P. Leonard，计算机。方法。应用。机械。 Eng。，19，（1979），59-98]，是针对一般非线性保护定律的积分形式的三阶（不是二阶）有限体积方案，其中具有数值溶液的点价值溶液。三阶精度通过仔细且详细的截断误差分析证明，并通过一系列彻底的数值测试证明。快速方案需要对时间导数进行仔细的空间离散化，以保护不稳定问题的三阶准确性。讨论了两种技术，包括伦纳德的最快计划。讨论如何错误地发现快速方案是二阶准确的。本文旨在作为参考，以阐明有关快速方案三阶准确性的任何混乱，也是阐明三阶非结构网格方案的基础，正如我们将在随后的论文中讨论的那样。
In this paper, we resolve the ever-present confusion over the QUICK scheme: it is a second-order scheme or a third-order scheme. The QUICK scheme, as proposed in the original reference [B. P. Leonard, Comput. Methods. Appl. Mech. Eng., 19, (1979), 59-98], is a third-order (not second-order) finite-volume scheme for the integral form of a general nonlinear conservation law with point-valued solutions stored at cell centers as numerical solutions. Third-order accuracy is proved by a careful and detailed truncation error analysis and demonstrated by a series of thorough numerical tests. The QUICK scheme requires a careful spatial discretization of a time derivative to preserve third-order accuracy for unsteady problems. Two techniques are discussed, including the QUICKEST scheme of Leonard. Discussions are given on how the QUICK scheme is mistakenly found to be second-order accurate. This paper is intended to serve as a reference to clarify any confusion about third-order accuracy of the QUICK scheme and also as the basis for clarifying third-order unstructured-grid schemes as we will discuss in a subsequent paper.
