期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

随机Burgers方程的有限体积方法 被引量：1

Finite Volume Method for Stochastic Burgers Equation
在线阅读 下载PDF
导出
摘要 本文应用有限体积方法研究带有不确定性输入参数的Burgers方程,其特点是在时间离散上采用二阶有限差分,在控制体上对非线性对流项采用不同的定义方式.在边界条件和粘性系数存在随机扰动的情况下,通过数值模拟验证了算法的收敛性和稳定性,并进一步测试了通过加密空间网格点的方法来抑制边界和粘性系数扰动对计算结果的影响. In this paper, we use the finite volume method to numerically solve the Burgers equation with uncertain input data. Firstly, an efficient numerical algorithm is proposed by using the second order finite difference in the time discretization and finite volume schemes in the spatial discretization, respectively. The main idea to use the different definition mode for nonlinear convection term. Secondly, when the boundary condition and the viscosity coefficient have a random perturbation, the stability and convergence of the new scheme are analyzed and verified. Finally, we make a conclusion that the influence of the stochastic disturbance on the boundary condition or viscosity coefficient in numerical calculation can be controlled by increasing the number of grid points.
作者 哈里曼.达力汗 冯新龙
机构地区 厦门大学数学科学学院 新疆大学数学与系统科学学院
出处 《工程数学学报》 CSCD 北大核心 2013年第1期49-58,共10页 Chinese Journal of Engineering Mathematics
基金 国家自然科学基金(61163027 10901131) 新疆少数民族特培基金(201123117) 新疆大学自然科学基金(XY080102)~~
关键词 BURGERS方程 有限体积方法 三层格式 随机扰动 Burgers equation finite volume method three-layer schemes stochastic distur-bance
分类号 O175 [理学—基础数学] O241.82 [理学—计算数学]
  • 相关文献

参考文献12

  • 1Fletcher C A. A comparison of finite element and finite difference solution of the one-and two-dimensional Burger's equations[J].{H}Journal of Computational Physics,1983,(01):159-188.
  • 2Maday Y,Quarteroni A. Approximation of Burgers' equation by pseudospectral mothods[J].ESAIM:Math-ematical Modelling and Numerical Analysis-Modélisation Mathématiqueet Analyse Numérique,1982,(04):375-402.
  • 3Ma H P,Guo B Y. The Chebyshev spectral method for Burgers-like equation[J].{H}Journal of Computational Mathematics,1988,(01):48-53.
  • 4Feistauer M,Felcman J,Medvidova M L. On the convergence of a combined finite volume-finite element method for nonlinear convection diffusion problems[J].Numerical Methods for Partial Differential Equa-tions,1997,(02):163-190.
  • 5Cordero E,Biase D L,Pennati V. A new finite volume method for the solution of convection diffusion equations:analysis of stability and convergence[J].{H}COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING,1997,(12):923-940.
  • 6Chorin A J. Hermite expansion in Monte-Carlo simulations[J].{H}Journal of Computational Physics,1971,(03):472-482.
  • 7Babuska I,Tempone R,Zouraris G E. Galerkin finite element approximations of stochastic elliptic partial differential equations[J].SIAM Journal on Numerical Analysis,2004,(02):800-825.doi:10.1137/S0036142902418680.
  • 8Babuska I,Tempone R,Zouraris G E. Solving elliptic boundary value problems with uncertain coe?cients by the finite element method:the stochastic formulation[J].{H}Computer Methods in Applied Mechanics and Engineering,2002,(12-16):1251-1294.
  • 9Deb M K,Babuska I M,Oden J T. Solution of stochastic partial differential equations using Galerkin finite element technique[J].{H}Computer Methods in Applied Mechanics and Engineering,2001,(48):6359-6372.
  • 10Frauenfelder P,Schwab C,Todor R A. Finite elements for elliptic problems with stochastic coe?cients[J].{H}Computer Methods in Applied Mechanics and Engineering,2005,(2-5):205-228.

同被引文献11

  • 1Reed W H, Hill T R. Triangular mesh methods for the neutron transport equation[R]. Technical Report, LA-UR-73-479, Los Alamos Scientific Laboratory, 1973.
  • 2Cockburn B, Hou S, Shu C W. TVB Runge-Kuta local discontinuous Calerkin finite element method for conservation laws IV: the multidimensional case[J]. Mathematics of Computation, 1990, 54(190): 545-581.
  • 3Cockburn B, Lin S Y, Shu C W. TVB Runge-Kutta local projection discontinuous Calerkin finite element method for conservation laws III: one dimensional systems[J]. Journal of Computational Physics, 1989, 84(1): 90-113.
  • 4Cockburn B, Shu C W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for scalar conservation laws II: general framework[J]. Mathematics of Computation, 1989, 52(186): 411-435.
  • 5Cockburn B, Shu C W. The Runge-Kutta local projection Pl-discontinuous Galerkin method for scalar conservation laws[J]. Mathematical Modelling and Numerical Analysis, 1991, 25(3): 337-361.
  • 6Warburton T C, Lomtev I, Kirby R M, et al. A discontinuous Galerkin method for the Navier-Stokes equations on hybrid grids[R]. Center for Fluid Mechanics #97-114, Division of Applied Mathematics, Brown University, 1997.
  • 7Zhang Q, Shu C W. Error estimates to smooth solutions of Runge-Kutta discontinuous Galerkin methods for scalar conservation laws[J]. SIAM Journal on Numerical Analysis, 2004, 42(2): 641-666.
  • 8Xu Y, Shu C W. Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-diffusion and Kdv equations[J]. Computer Methods in Applied Mechanics and Engineering, 2007, 196(37-40): 3805-3822.
  • 9Cockburn B, Kanschat G, Perugia I, et al. Superconvergence of the local discontinuous Galerkin method for elliptic problems on Cartesian grids[J]. SIAM Journal on Numerical Analysis, 2001, 39(1): 264-285.
  • 10Wu F, Feng X L, Liu D. The local discontinuous Galerkin finite element method for a class of convection- diffusion equations[J]. Nonlinear Analysis: Real World Applications, 2013, 14(1): 734-752.

引证文献1

工程数学学报
2013年 第1期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部