上风逐部分求和有限差分:误差估算和 WENO 方法

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
Yan Jiang, Siyang Wang
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引用次数: 0

摘要

最近开发出了高阶上风逐部求和有限差分算子。当与施加边界条件的同时逼近项法相结合时,该方法的收敛速度比使用传统的逐部求和算子更快。我们通过法模分析证明了这类方法对一类双曲偏微分方程的收敛速度。我们的分析表明,施加边界条件的惩罚参数会影响稳定方法的收敛速度。此外,为了解决数据不连续的问题,我们扩展了该方法,使其也具有加权本质非振荡特性。整个方法是稳定的,对平滑问题达到了高阶精度,并能解决不连续问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Upwind Summation-by-parts Finite Differences: error Estimates and WENO methodology

Upwind Summation-by-parts Finite Differences: error Estimates and WENO methodology

High order upwind summation-by-parts finite difference operators have recently been developed. When combined with the simultaneous approximation term method to impose boundary conditions, the method converges faster than using traditional summation-by-parts operators. We prove the convergence rate by the normal mode analysis for such methods for a class of hyperbolic partial differential equations. Our analysis shows that the penalty parameter for imposing boundary conditions affects the convergence rate for stable methods. In addition, to solve problems with discontinuous data, we extend the method to also have the weighted essentially nonoscillatory property. The overall method is stable, achieves high order accuracy for smooth problems, and is capable of solving problems with discontinuities.

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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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