A Novel High-Order Immersed Boundary Method Based on Filter and Deconvolution Operation
-
摘要: 传统浸没边界法在边界附近只有一阶精度,而高精度的改进方法都需要额外引入跳跃条件,因此不具备普适性.文中设计了一种基于过滤和反卷积的新型算法,既在一定程度上提高了精度,又避免了以往方法中引入额外跳跃条件的难题.通过一个简单的一维算例验证了新算法可以达到接近二阶精度,其具体的精度值与反卷积步骤中选取的逆核函数在积分域边界的连续性有关.Abstract: The traditional immersed boundary method has only first-order accuracy near boundary. Existing improvements need additional jump conditions thus are not general. A novel method based on filter and deconvolution was introduced. It improved the accuracy, and avoided the problems of jump conditions. A simple 1-D case was performed to proove that the accuracy was nearly second order. It is found that the exact order value depends on the boundary continuity of the inverse kernel function chosen in deconvolution.
-
Key words:
- immersed boundary method /
- deconvolution /
- filter
-
[1] Cockburn B, Shu C W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II:general framework[J]. Math Comp,1989, 52(186): 411-435. [2] Cockburn B, Shu C W. Runge-Kutta Discontinuous Galerkin methods for convection-dominated problems[J].Journal of Scientific Computing,2001, 16(3): 173-261. [3] 蔚喜军, 周铁. 流体力学方程的间断有限元方法[J]. 计算物理, 2005, 22(2):108-116.(YU Xi-jun, ZHOU Tie. Discontinuous finite element methods for solving hydrodynamic equations[J].Chinese Journal of Computational Physics,2005, 22(2): 108-116.(in Chinese)) [4] 陈二云, 马大为. 间断有限元在弹尾超音速喷流计算中的应用[J]. 计算物理, 2008, 25(6):705-710.(CHEN Er-yun, MA Da-wei. Discontinuous finite element method for supersonic flow of a missile propulsive jet[J].Chinese Journal of Computational Physics,2008, 25(6): 705-710.(in Chinese)) [5] 何朝葵, 速宝玉, 盛金昌. 稳定渗流分析的局部间断伽辽金有限元法[J]. 河海大学学报(自然科学版), 2012, 40(2):206-210.(HE Zhao-kui, SU Bao-yu, SHENG Jin-chang. Local discontinuous Galerkin finite element method for steady seepage analysis[J].Journal of Hohai University(Natural Sciences),2012, 40(2): 206-210.(in Chinese)) [6] 徐云, 蔚喜军.自适应间断有限元方法求解双曲守恒律方程[J].计算物理,2009, 26(2):159-168.(XU Yun, YU Xi-jun. Adaptive discontinuous Galerkin methods for hyperbolic conservation laws[J]. Chinese Journal of Computational Physics,2009, 26(2): 159-168.(in Chinese)) [7] 郝海兵, 杨永, 李喜乐. p-型多重网格间断Galekin有限元方法研究[J]. 空气动力学学报, 2010, 12(6):715-719.(HAO Hai-bing, YANG Yong, LI Xi-le. The research of p-multigrid solution for high-order discontinuous Galerkin finite element method[J]. Acta Aerodynamica Sinica,2010, 12(6): 715-719.(in Chinese)) [8] Minchev B V,Wright W M. A review of exponential integrators for first order semi-linear problems[R]. NTNU: Tech Rep, 2005: 1-44. [9] Celledoni E, Marthinsen A, Owren B. Commutator-free Lie group methods[J]. Future Generation Computer Systems,2003, 19(3): 341-352. [10] Kassam A K, Trefethen L N. Fourth-order time-stepping for stiff PDEs[J].SIAM J Sci Comput,2005, 26(4): 1214-1233. [11] Hochbruck M, Ostermann A, Schweitzer J. Exponential Rosenbrock-type methods[J]. SIAM J Numer Anal,2009, 47(1): 786-803. [12] Hochbruck M, Ostermann A. Exponential integrators[J].Acta Numerica,2010, 19: 209-286. [13] Hesthaven J S, Warburton T.Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications [M].New York: Springer, 2008. [14] Gottlieb S,Shu C W. Total variation diminishing Runge-Kutta schemes[J]. Mathematics of Computation,1998, 67(221): 73-85. [15] Caliari M, Ostermann A. Implementation of exponential Rosenbrock-type integrators[J].Applied Numerical Math,2009, 59(3): 568-581. [16]
点击查看大图
计量
- 文章访问数: 1516
- HTML全文浏览量: 81
- PDF下载量: 1206
- 被引次数: 0