一维Euler方程的特征有限体积格式

郭彦; 刘儒勋

一维Euler方程的特征有限体积格式

郭彦,
刘儒勋

中国科学技术大学数学系,合肥 230026

基金项目: 国家自然科学基金资助项目(10771134)

详细信息

作者简介:
郭彦(1982- ),男,安徽人,博士(联系人.E-mail:gysx@mail.ustc.edu.cn).

中图分类号: O241.8；O352
计量
- 文章访问数: 3194
- HTML全文浏览量: 159
- PDF下载量: 1367
- 被引次数: 0
出版历程
- 收稿日期: 2008-07-04
- 修回日期: 2009-02-12
- 刊出日期: 2009-03-15

Characteristic-Based Finite Volume Scheme for 1D Euler Equations

GUO Yan,
LIU Ru-xun

Department of Mathematics, University of Science and Technology of China, Hefei 230026, P. R. China

摘要

摘要: 提出了一种用于求解一维标量方程和无粘Euler方程组的高阶有限体积格式．其中时间离散采用Simpson数值积分公式从而实现时间上的高阶．利用特征线理论得到网格节点在各个时间层沿着特征线的位置，而积分公式中的节点值通过三阶和五阶的中心加权本质无震荡重构得到．最后，给出了几个数值算例验证此方法的高精度和收敛性以及捕获激波的能力．
- 双曲方程 /
- 有限体积方法 /
- 特征理论 /
- WENO重构 /
- Runge-Kutta方法
Abstract: A highorder finitevolume scheme was presented for the onedimensional scalar and inviscid Euler conservation laws. The Simpson's quadrature rule was used to achieve highorder accuracy in time. To get the point value of the Simpson's quadrature, the characteristic theory was used to obtain the positions of the grid points at each sub-time stages along the characteristic curves, and the thirdorder and fifth-order central weighted essentially non-oscillatory (CWENO) reconstruction was adopted to estimate the cell point values. Several standard one-dimensional examples were used to verify highorder accuracy, convergence and capability of capturing shock.
- hyperbolic equation /
- finite volume method /
- characteristic theory /
- WENO reconstruction /
- Runge-Kutta method

HTML全文

参考文献(13)

[1]	Shu C W,Osher S.Efficient implementation of essentially non-oscillatory shock capturing schemes[J].J Comput Phys,1988,77(2):439-471. doi: 10.1016/0021-9991(88)90177-5
[2]	Shu C W,Osher S.Efficient implementation of essentially non-oscillatory shock capturing schemes Ⅱ[J].J Comput Phys,1989,83(1):32-78. doi: 10.1016/0021-9991(89)90222-2
[3]	Jiang G,Shu C W.Efficient implementation of weighted ENO schemes[J]. J Comput Phys,1996,126(1):202-228. doi: 10.1006/jcph.1996.0130
[4]	Levy D,Pupo G,Russo G.Compact central WENO schemes for multidimensional conservation laws[J].SIAM J Sci Comput,2000,22(2):656-672. doi: 10.1137/S1064827599359461
[5]	Capdeville G.A central WENO scheme for solving hyperbolic conservation laws on non-uniform meshes[J].J Comput Phys,2008,227(5):2977-3014. doi: 10.1016/j.jcp.2007.11.029
[6]	陈荣三.大密度和大压力比可压缩的数值计算[J].应用数学和力学，2008,29(5):609-617.
[7]	涂国华，袁湘江，陆利蓬.激波捕捉差分方法研究[J].应用数学和力学，2007,28(4):433-440.
[8]	HU Jun,GUO Shao-gang.Solution to Euler equations by high-resolution upwind compact scheme based on flux splitting[J]. Internat J Numer Meth Fluids,2008,56(11):2139-2150. doi: 10.1002/fld.1611
[9]	Xiao F,Peng X. A convexity preserving scheme for conservative advection transport[J].J Comput Phys,2004,198(2):389-402. doi: 10.1016/j.jcp.2004.01.013
[10]	Ii S,Xiao F. CIP/multi-moment finite volume method for Euler equations:A semi-Lagrangian characteristic formulation[J]. J Comput Phys,2007,222(2):849-871. doi: 10.1016/j.jcp.2006.08.015
[11]	Qiu J,Shu C W. Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method:one dimensional case[J].J Comput Phys,2004,193(1):115-135. doi: 10.1016/j.jcp.2003.07.026
[12]	Lax P D. Weak solutions of nonlinear hyperbolic equations and their numerical computation[J].Commun Pure Appl Math,1954,7(1):198-232.
[13]	Sod G. A survey of several finite difference methods for systems of non-linear conservation laws[J].J Comput Phys,1978,27(1):1-31. doi: 10.1016/0021-9991(78)90023-2