用于双曲守恒定律和高度振荡问题的新型混合三角 WENO 方案

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2024-10-17 DOI:10.1016/j.aml.2024.109339

Liang Li , YanMeng Wang , Jun Zhu

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引用次数: 0

摘要

在传统的混合 WENO 方案中，需要计算高阶多项式的极值点，由于难以确定高阶三角多项式的极值点，这给将该方法扩展到混合三角 WENO（TWENO）方案带来了挑战。在本文中，我们提出了一种新颖的混合策略，它规避了寻找高阶多项式极值点的必要性，只需要三个低阶多项式的极值点。基于这种混合策略，我们设计了两种混合 TWENO 方案，这两种方案都显著提高了 TWENO 方案的数值模拟性能，同时节省了约 80% 的计算时间。

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A new hybrid trigonometric WENO scheme for hyperbolic conservation laws and highly oscillatory problems

In the conventional hybrid WENO scheme, the computation of extremum points of high-order polynomials is required, which poses challenges when extending this methodology to the hybrid trigonometric WENO (TWENO) scheme due to the difficulties in determining the extremum points of high-order trigonometric polynomials. In this paper, we propose a novel hybrid strategy that circumvents the necessity of finding extremum points of high-degree polynomials, requiring only the extremum points of three lower-order polynomials. Based on this hybrid strategy, two hybrid TWENO schemes are designed, both of which significantly improve the numerical simulation performance of the TWENO scheme while saving approximately 80% of the computation time.

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.