数值计算与计算机应用
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数值计算与计算机应用  2015, Vol. 36 Issue (1): 12-21    DOI:
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一类基于插值误差的多尺度水平集方法
唐玲艳, 宋松和
国防科学技术大学理学院数学与系统科学系, 长沙 410073
A CLASS OF MULTISCALE LEVEL SET METHODS BASED ON INTERPOLATING ERRORS
Tang Lingyan, Song Songhe
Department of Mathematics and System Science, Science school, National University of Defence Technology, Changsha 410073, China
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摘要 本文对嵌套网格上水平集函数的符号函数进行插值, 利用插值误差建立运动界面流场的离散多分辨分析, 根据多分辨系数确定局部网格尺度和计算格式, 构造了一类多尺度水平集方法. 对于多分辨系数较大的运动界面附近区域, 采用高精度WENO格式进行时间推进, 其余区域则直接采用多项式插值. 与单一尺度的水平集方法相比, 该方法可以在较少的CPU计算时间内捕捉到更为精细、锐利的运动界面.
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关键词水平集方法   多尺度   自适应计算     
Abstract: In this paper, a discrete multiresolution analysis of the flow field with moving interface is built up based on the interpolating errors of the sign function of level set function on a nested grid structure. By using the multiresolution coefficients to establish the local grid size and computational scheme, we constructe a class of multiscale level set methods. For flow region near the moving interface where the magnitudes of the multiresolution coefficients are large, the high-order WENO scheme is used for time evolution. While in the rest computational region, solutions are obtained directly by polynomial interpolation. Compared with the single-scale level set method, this method can capture more sophisticated and sharper motion interface with less CPU expenses.
Key wordsLevel set method   multiscale   adaptive computation   
收稿日期: 2014-02-27;
基金资助:

国家自然科学基金(11001027, 91130013, 61171018)及空气动力学国家重点实验室开放课题资助项目.

引用本文:   
. 一类基于插值误差的多尺度水平集方法[J]. 数值计算与计算机应用, 2015, 36(1): 12-21.
. A CLASS OF MULTISCALE LEVEL SET METHODS BASED ON INTERPOLATING ERRORS[J]. Journal of Numerical Methods and Computer Applicat, 2015, 36(1): 12-21.
 
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