二维群集Vicsek模型的动理学方程的一个二阶精度格式  

A Second-order Accurate Scheme for a Kinetic Equation of Two-dimensional Vicsek Swarming Model

作　　者：段俊明 汤华中[1,2] DUAN Jun-ming;TANG Hua-zhong(School of Mathematical Sciences,Peking University,Beijing100871;School of Mathematics and Computational Science,Xiangtan University,Xiangtan411105 China)

机构地区：[1]北京大学数学科学学院,北京100871 [2]湘潭大学数学与计算科学学院,湖南湘潭411105

出　　处：《湘潭大学学报（自然科学版）》2019年第1期1-14,共14页Journal of Xiangtan University(Natural Science Edition)

基　　金：国家自然科学基金项目(91630310;11421101)

摘　　要：提出了求解二维群集Vicsek模型的动理学方程的一个二阶精度格式,其中二阶精度的算子分裂技术用于解耦对流项和碰撞项,高分辨MUSCL格式用于对流项的离散,而谱方法和二阶隐式龙格库塔方法分别用于在速度和时间方向近似碰撞部分子问题.给出了几个用于检验格式精度和有效性的一维和二维数值实验.数值结果表明,所提出的格式具有二阶精度;与文[J Comput Phys,2015,297:32-46]中的一阶格式比,它能较好地分辨黎曼问题解中的间断.This paper proposes a second-order accurate scheme for the two-dimensional kinetic equation of Vicsek swarming model.The operator splitting technique is used to decouple the convective term and collision part,and the former is approximated by using the high-resolution MUSCL scheme,while the spectral and implicit Runge-Kutta methods are employed to discretize the latter in the velocity and time respectively.Several 1 Dand 2 Dnumerical experiments are conducted to demonstrate the accuracy and effectiveness of our scheme.The results show that our scheme is second order accurate and well resolves the discontinuities in the Riemann problems.

关 键 词：群集模型 Vicsek模型 动理学方程 谱方法 MUSCL 

分 类 号：O411[理学—理论物理]