删除或更新信息,请邮件至freekaoyan#163.com(#换成@)

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

本站小编 Free考研考试/2021-12-27

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
收稿日期:2016-11-01出版日期:2017-08-15发布日期:2017-08-04


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.


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
Received:2016-11-01Online:2017-08-15Published:2017-08-04







摘要



编辑推荐
-->


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.
MR(2010)主题分类:
65D17

分享此文:


()

[1] Friedrichs O. Weighted essentially non-oscillatory schemes for the interpolation of mean values on unstructured grids[J]. J. Comput. Phys, 1998, 144(1): 194-212.

[2] Abgrall R. On Essentially Non-oscillatory Schemes on Unstructured Meshes: Analysis and Implementation[J]. J. Comput. Phys, 1994, 114(1): 45-58.

[3] Hu C, Shu C W. Weighted essentially non-oscillatory schemes on triangular meshes[J]. J. Comput. Phys., 150(1): 97-127.

[4] Wolf W R M, Azevedo J L F. High order ENO and WENO schemes for unstructured grids[J]. Int. J. Numer. Mech. Fluids, 2007, 55(10): 917-943.

[5] Zhang Y T, Shu C W. Third Order WENO Scheme on Three Dimensional Tetrahedral Meshes[J]. Comm. Comp. Phys., 2009, 5(2-4): 836-848.

[6] Zhang X, Shu C W. On maximum-principle-satisfying high order schemes for scalar conservation laws[J]. J. Comput. Phys., 2010, 229(9): 3091-3120.

[7] Zhang X, Shu C W. On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes[J]. J. Comput. Phys., 2010, 229(23): 8918-8934.

[8] Zhang X X, Xia Y H, Shu C W. Maximum-principle-satisfying and positivity-preserving high order discontinuous Galerkin schemes for conservation laws on triangular meshes[J]. J. Sci. Comp., 2012, 50(1): 29-62.

[9] Xiong T, Qiu J M, Xu Z. A parametrized maximum principle preserving flux limiter for finite difference RK-WENO schemes with applications in incompressible flows[J]. J. Comput. Phys., 2013, 252(11): 310-331.

[10] Christlieb A, Liu Y, Tang Q, Xu Z F. High order parametrized maximum-principle-preserving and positivity-preserving WENO schemes on unstructured meshes[J]. J. Comput. Phys., 2015, 281: 334-351.

[11] 张来平, 刘伟, 贺立新, 邓小刚, 张涵信. 一种新的间断侦测器及其在DGM中的应用[J]. 空气动力学报, 2011, 29(4): 401-406.

[12] Cockbu宋松和, 李荫藩. 解二维标量双曲型守恒律的一类满足极值原理的无结构三角形网格有限体积法[J]. 数值计算与计算机应用, 1997, 18(2): 106-113.

[13] 唐玲艳, 傅浩, 宋松和. 三维非结构网格上求解双曲型守恒律方程的一类三阶精度有限体积格式[J]. 数值计算与计算机应用, 2013, 34(3): 212-220.

[14] Cockburn B, Shu C W. Runge-Kutta discontinuous Galerkin methods for convection-dominated problems[J]. J. Scientific Comput., 2001, 16: 173-261.

[1]甘小艇, 殷俊锋. 二次有限体积法定价美式期权[J]. 计算数学, 2015, 37(1): 67-82.
[2]谢春梅, 骆艳, 冯民富. Darcy-Stokes问题的统一稳定化有限体积法分析[J]. 计算数学, 2011, 33(2): 133-144.
[3]朱华君, 陈亚铭, 宋松和, 唐贻发. 二维非线性Schrödinger方程的辛与多辛格式[J]. 计算数学, 2010, 32(3): 315-326.
[4]于长华, 李永海. 解Poisson方程的基于应力佳点的双二次元有限体积法[J]. 计算数学, 2010, 32(1): 59-74.
[5]张文博,孙澈. 线性定常对流占优对流扩散问题的有限体积——流线扩散有限元法[J]. 计算数学, 2004, 26(1): 93-8.
[6]李永海. 抛物方程的一种广义差分法(有限体积法)[J]. 计算数学, 2002, 24(4): 487-500.
[7]汤华中. 一个刚性守恒律方程组的全隐式差分方法[J]. 计算数学, 2001, 23(2): 129-138.
[8]胡健伟. 非自伴椭圆问题的离散强极值原理与区域分解法[J]. 计算数学, 1999, 21(3): 283-292.

--> -->
阅读次数
全文







摘要





Cited

Shared






PDF全文下载地址:

http://www.computmath.com/jssx/CN/article/downloadArticleFile.do?attachType=PDF&id=216
相关话题/计算 数学 结构 国防科技大学 交通