论文标题
一种新的WENO-2R算法，具有渐进的准确性顺序接近不连续性
A new WENO-2r algorithm with progressive order of accuracy close to discontinuities
论文作者
论文摘要
在本文中，我们介绍了对[S. Amat，J。Ruiz，C.-W。 Shu，在新的WENO算法2R的新算法上，其准确性已取得了不连续性的提高，应用程序。数学。 Lett。 105（2020），106-298]。在上述工作中，我们设法获得了一种算法，该算法达到了渐进式和最佳的准确度，接近Weno-6的不连续性。对于更高的订单，即WENO-8，WENO-10等。我们发现，以前的算法在检测不连续性时会呈现一些阴影，这意味着，准确性的顺序比Weno所达到的同一顺序的序列要好，但不是最佳的。在本文中，我们介绍了原始算法中使用的平滑度指标的修改，该指标定向解决此问题，并以接近不连续性的准确性逐步准确地达到WENO-2R算法。我们还提供了证明准确性和明确公式的所有权重，用于该算法的任何阶2R的所有权重。
In this article we present a modification of the algorithm for data discretized in the point values introduced in [S. Amat, J. Ruiz, C.-W. Shu, On a new WENO algorithm of order 2r with improved accuracy close to discontinuities, App. Math. Lett. 105 (2020), 106-298]. In the aforementioned work, we managed to obtain an algorithm that reaches a progressive and optimal order of accuracy close to discontinuities for WENO-6. For higher orders, i.e. WENO-8, WENO-10, etc. We have found that the previous algorithm presents some shadows in the detection of discontinuities, meaning that the order of accuracy is better than the one attained by WENO of the same order, but not optimal. In this article we present a modification of the smoothness indicators used in the original algorithm, oriented to solve this problem and to attain a WENO-2r algorithm with progressive order of accuracy close to the discontinuities. We also present proofs for the accuracy and explicit formulas for all the weights used for any order 2r of the algorithm.
