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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/mathematics-engineers-capstone
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课程名称：工程师的数学：顶点课程 课程概述： 《工程师的数学：顶点课程》为完成工程师数学专业化的学生提供了一个顶点项目。学生将首先学习一些基本的计算流体动力学概念，然后应用这些概念计算绕圆柱体的流体流动。所有注册的学生均可访问在线MATLAB及MATLAB评分工具。在注册之前，学生应已完成矩阵代数、微分方程、向量微积分和数值方法课程，并能够进行MATLAB编程。 本课程包括22个简短的视频讲座和一整套讲义。每节课后都有解题任务，并在第二和第三周末有相当量的MATLAB编程作业。 下载讲义链接： http://www.math.ust.hk/~machas/flow-around-a-cylinder.pdf 观看宣传视频： https://youtu.be/FlM1de9Sxh0 课程大纲： 1. **控制方程（Governing Equations）**： 学习圆柱体周围流动的控制方程，讨论纳维-斯托克斯方程和连续性方程，推导出流函数和标量涡度的耦合方程。对这些方程进行无量纲化，使其包含一个称为雷诺数的无量纲参数，并使用对数极坐标简化无量纲控制方程。 2. **稳态流动（Steady Flows）**： 制定圆柱体周围稳态流动的计算流体动力学问题，介绍有限差分法并推导迭代方程。推导边界条件，讨论MATLAB程序的框架。学生将编写MATLAB代码以计算雷诺数为10时的流函数。 3. **非稳态流动（Unsteady Flows）**： 制定圆柱体周围非稳态流动的计算流体动力学问题，引入极角的周期边界条件，并展示如何使用矩阵方法求解流函数。演示如何使用MATLAB ODE积分器来求解标量涡度。学生将编写MATLAB代码以计算雷诺数为60时的时变标量涡度。 该课程适合希望将数学知识应用于工程领域的学生，通过实际项目加深对流体动力学的理解与实践能力。
Name:Governing Equations
Description:We learn the governing equations for the flow around a cylinder. We discuss the Navier-Stokes equations and the continuity equation, and derive a pair of coupled equations for the stream function and scalar vorticity. We nondimensionalize these equations so that they contain only a single dimensionless parameter called the Reynolds number. We then simplify the nondimensional governing equations using log-polar coordinates.
Name:Steady Flows
Description:We formulate the computational fluid dynamics problem of the steady flow around a cylinder. We introduce the finite difference method and derive iteration equations. We derive boundary conditions and discuss the outline of a MATLAB program. Students will write a MATLAB code to compute the stream function at a Reynolds number of ten.
Name:Unsteady Flows
Description:We formulate the computational fluid dynamics problem of the unsteady flow around a cylinder. We introduce periodic boundary conditions in the polar angle, and show how to solve for the stream function using matrix methods. We show how to use a MATLAB ODE integrator to solve for the scalar vorticity. Students will write a MATLAB code to compute the time-dependent scalar vorticity at a Reynolds number of sixty.
Mathematics for Engineers: The Capstone Course provides a capstone project for students who are completing the Mathematics for Engineers specialization. Students will first learn some basic concepts in computational fluid dynamics, and then apply these concepts to compute the fluid flow around a cylinder. Access to MATLAB online and the MATLAB grader is given to all students who enroll. Before enrolling, students should have already taken courses in matrix algebra, differential equations, vector calculus and numerical methods and be able to program in MATLAB. The course contains 22 short video lectures and a full set of lecture notes. After each lecture there are problems to solve and at the end of the second and third weeks there is a substantial MATLAB programming assignment. Download the lecture notes: http://www.math.ust.hk/~machas/flow-around-a-cylinder.pdf Watch the promotional video: https://youtu.be/FlM1de9Sxh0
