斯托克斯第一问题的有限差分法的MATLAB实现  

MATLAB Implementation of the Finite Difference Method for Stokes First Problem

作　　者：陈庚 CHEN Geng(North Minzu University,Yinchuan 750030,China)

机构地区：[1]北方民族大学,宁夏银川750030

出　　处：《现代信息科技》2023年第20期58-61,共4页Modern Information Technology

基　　金：宁夏回族自治区大学生创新训练项目(S202211407040)。

摘　　要：斯托克斯方程是流体力学中描述粘性牛顿流体运动的方程组,在航空航天、流体力学、化工工程、生物工程等与流体有关的所有领域都有着非常重要的作用和广泛的应用。有限差分方法通过离散物理问题,从而以代数方程式的形式来求解出误差较小的近似数值解。文章给出斯托克斯第一问题使用有限差分法和MATLAB矩阵运算的计算方法,通过对网格进行二维剖分细化,借用计算机的强大算力得出稳定性条件下的速度曲线,并使用相关算例进一步确定扩散数的阈值。The Stokes equations are a set of equations describing the motion of viscous Newtonian fluids in fluid mechanics and have a very important role and wide application in allfields related tofluids such as aerospace,fluid mechanics,chemical engineering and bioengineering.The finite difference method solves approximate numerical solutions with small errors in algebraic equation form by discretizing the physical problem.This paper gives a computational approach to the Stokesfirst problem using thefinite difference method and MATLAB matrix operations to derive the velocity profile under stability conditions by refining the grid with a two-dimensional profile,borrowing the power of computer arithmetic,and using relevant arithmetic examples to further determine the threshold value of the diffusion number.

关 键 词：有限差分法 斯托克斯问题 MATLAB 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]