计算数学
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计算数学  2017, Vol. 39 Issue (3): 309-320    DOI:
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非结构网格上一类满足局部极值原理的三阶精度有限体积方法
唐玲艳, 郭云瑞, 宋松和
NUDT, 国防科技大学理学院 数学与系统科学系, 长沙 410073
A CLASS OF THIRD ORDER FINITE VOLUME SCHEME SATISFYING THE LOCAL MAXIMUM PRINCIPLE ON UNSTRUCTURED MESHES
Tang Lingyan, Guo Yunrui, Song Songhe
Department of Mathematics and System Science, Science School, National University of Defence Technology, Changsha 410073, China
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摘要 对二维标量双曲型守恒律方程,发展了一类满足局部极值原理的非结构网格有限体积格式.其构造思想是,以单调数值通量为基础,通过应用基于最小二乘法的二次重构和极值限制器,使数值解满足局部极值原理.为保证数值解在光滑区域达到三阶精度,该格式可结合局部光滑探测器使用.本文从理论上分析了格式的稳定性条件,数值实验验证了格式的精度和对间断的分辨能力.
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关键词双曲型守恒律   有限体积法   极值原理   限制器     
Abstract: A third order finite volume scheme is constructed for scalar hyperbolic conservation laws on two dimensional unstructured meshes. The scheme is based on monotone numerical flux and is particularly straightforward to implement. By applying the quadratic reconstruction based on the least square method and the maximum limiter, the numerical solution can satisfy the local maximum principle. To obtained third order accuracy in the smooth region, the proposed scheme can be used in combination with the local smooth detector. In this paper, the stability condition of the scheme is analyzed theoretically, and its accuracy and the ability of capturing singularities are verified by numerical experiments.
Key wordshyperbolic conservation laws   finite volume method   maximum principle   limiter   
收稿日期: 2016-11-01;
基金资助:

国家自然科学基金(11571366),国防科技大学校科研计划(ZK16-03-53)和长沙理工大学综合交通大数据智能处理湖南省重点实验室开放基金资助项目.

引用本文:   
. 非结构网格上一类满足局部极值原理的三阶精度有限体积方法[J]. 计算数学, 2017, 39(3): 309-320.
. A CLASS OF THIRD ORDER FINITE VOLUME SCHEME SATISFYING THE LOCAL MAXIMUM PRINCIPLE ON UNSTRUCTURED MESHES[J]. Mathematica Numerica Sinica, 2017, 39(3): 309-320.
 
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