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首页> 外文期刊>SIAM Journal on Scientific Computing >HYBRID COMPACT-WENO FINITE DIFFERENCE SCHEME WITH RADIAL BASIS FUNCTION BASED SHOCK DETECTION METHOD FOR HYPERBOLIC CONSERVATION LAWS
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HYBRID COMPACT-WENO FINITE DIFFERENCE SCHEME WITH RADIAL BASIS FUNCTION BASED SHOCK DETECTION METHOD FOR HYPERBOLIC CONSERVATION LAWS

机译：具有径向基函数的基于冲击检测方法的混合型紧凑型Weno有限差分方案

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摘要

A hybrid scheme, based on the high order nonlinear characteristicwise weighted essentially nonoscillatory (WENO) conservative finite difference scheme and the spectral-like linear compact finite difference scheme, has been developed for capturing shocks and strong gradients accurately and resolving fine scale structures efficiently for hyperbolic conservation laws. The key issue in any hybrid scheme is the design of an accurate, robust, and efficient high order shock detection algorithm which is capable of determining the smoothness of the solution at any given grid point and time. An improved iterative adaptive multiquadric radial basis function (IAMQ-RBF-Fast) method [W. S. Don, B. S. Wang, and Z. Gao, T. Sci. Comput, 75 (2018), pp. 1016-1039], which employed the O(N-2) recursive Levinson-Durbin method and the Sherman-Morrison-Woodbury method for solving the perturbed Toeplitz matrix system, has been successfully developed as an efficient and accurate edge detector of the piecewise smooth functions. In this study, the method, together with Tukey's boxplot method and the domain segmentation technique, is extended to serve as a novel shock detection algorithm for solving the Euler equations. The applicability and performance of the RBF edge detection method as the shock detector in the hybrid scheme in terms of accuracy, robustness, efficiency, resolution, and other implementation issues are given. Several one- and two-dimensional benchmark problems in shocked flow demonstrate that the proposed hybrid scheme can reach a speedup of the CPU times by a factor up to 2-3 compared with the pure fifth order WENO-Z scheme.
机译：基于高阶非线性的混合方案基本上是非振动（Weno）保守有限差分方案和光谱相同的线性紧凑型有限差分方案，用于精确地捕获冲击和强梯度，并有效地解决双曲线保护法。任何混合动力方案的关键问题是设计精确，坚固，高效的高阶冲击检测算法，其能够在任何给定的网格点和时间确定解决方案的平滑度。一种改进的迭代自适应多功率径向基函数（IAMQ-RBF-FAST）方法[W. S. Don，B. S. Wang和Z.Gao，T.Sci。计算，75（2018），第1016-1039页，它采用O（N-2）递归韦林顿 - 德宾方法和谢尔曼 - Morrison-Woodbury方法，用于解决扰动的Toeplitz矩阵系统，已成功开发为一个高效且精确的边缘检测器的分段平滑功能。在该研究中，该方法与Tukey的Boxpot方法和域分割技术一起扩展以用作求解欧拉方程的新型冲击检测算法。给出了RBF边缘检测方法的适用性和性能作为混合方案中的冲击探测器，在准确性，鲁棒性，效率，分辨率和其他实施问题方面。与纯第五阶WENo-Z方案相比，震动流动中的几个和二维基准问题证明所提出的混合体方案可以达到高达2-3的CPU次数的加速。

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