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The QUICK scheme is a third-order finite-volume scheme with point-valued numerical solutions
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-03-04 , DOI: 10.1002/fld.4975 Hiroaki Nishikawa 1
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-03-04 , DOI: 10.1002/fld.4975 Hiroaki Nishikawa 1
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In this paper, we resolve the ever-present confusion over the Quadratic Upwind Interpolation for Convective Kinematics (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 economical high-order unstructured-grid schemes as we will discuss in a subsequent paper.
中文翻译：
QUICK 方案是具有点值数值解的三阶有限体积方案
在本文中，我们解决了对流运动学二次逆风插值 (QUICK) 方案一直存在的困惑：它是二阶方案还是三阶方案。在原始参考文献 (BP Leonard, Comput. Methods. Appl. Mech. Eng., 19, (1979), 59-98) 中提出的 QUICK 方案是一个三阶（不是二阶）有限体积一般非线性守恒定律的积分形式的方案，点值解作为数值解存储在单元中心。三阶精度通过仔细和详细的截断误差分析得到证明，并通过一系列彻底的数值测试得到证明。QUICK 方案需要对时间导数进行仔细的空间离散化，以保持非定常问题的三阶精度。讨论了两种技术，包括 Leonard 的 QUICKEST 方案。讨论了如何错误地发现 QUICK 方案是二阶准确的。本文旨在作为参考，以澄清有关 QUICK 方案的三阶精度的任何混淆，并作为阐明经济的高阶非结构化网格方案的基础，我们将在随后的论文中讨论。
更新日期：2021-03-04
中文翻译：
QUICK 方案是具有点值数值解的三阶有限体积方案
在本文中，我们解决了对流运动学二次逆风插值 (QUICK) 方案一直存在的困惑：它是二阶方案还是三阶方案。在原始参考文献 (BP Leonard, Comput. Methods. Appl. Mech. Eng., 19, (1979), 59-98) 中提出的 QUICK 方案是一个三阶（不是二阶）有限体积一般非线性守恒定律的积分形式的方案，点值解作为数值解存储在单元中心。三阶精度通过仔细和详细的截断误差分析得到证明，并通过一系列彻底的数值测试得到证明。QUICK 方案需要对时间导数进行仔细的空间离散化，以保持非定常问题的三阶精度。讨论了两种技术，包括 Leonard 的 QUICKEST 方案。讨论了如何错误地发现 QUICK 方案是二阶准确的。本文旨在作为参考，以澄清有关 QUICK 方案的三阶精度的任何混淆，并作为阐明经济的高阶非结构化网格方案的基础，我们将在随后的论文中讨论。
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