An Introduction To Computational Fluid Dynamics (Cfd)

本课程将涵盖二维笛卡尔网格上不可压缩流的有限体积法的基础知识。主题包括离散化过程、插值技术、边界条件、使用 ParaView 的流动可视化以及 CFD 误差和不确定性。学生将编写三个代码；第一个代码解决了纯扩散问题，第二个解决了纯对流问题，第三个使用简单的压力-速度耦合程序解决了 Navier-Stokes 方程。Navier-Stokes 求解器将用于求解“驱动腔”问题，以及涉及通道中发展流动的问题。这三个代码也可供下载，例如，研究求解过程，或帮助调试学生编写的代码。

概述

第 1 节：简介

第 1 讲 CFD 简介以及我们将在本课程中介绍的内容。

第 2 讲 一些具有代表性的低成本 CFD 结果。

第 2 节：对有限差分近似和迭代方法的回顾。

第 3 讲 有限差分近似的推导

第 4 讲基本迭代求解器

第 3 节：扩散问题的有限体积法

第 5 讲 扩散项的离散化：第 1 部分

第 6 讲 扩散项的离散化：第 2 部分

第 7 讲 扩散项的离散化：边界条件

第 8 讲 一个示例问题

第 9 讲 Fortran 代码示例扩散问题

第 10 讲 Fortran 代码部分为 ParaView 编写 .csv 文件

第 11 讲 使用 ParaView 进行可视化

第 4 节：对流问题的有限体积法

第12讲对流项的离散化

第13讲插值方法：中心“差分”

第14讲插值方法：一阶上风

第 15 讲“混合”插值方案的延迟修正

第16讲 一个示例问题：描述

第17课示例问题的逆向分量边界条件

第18讲示例问题的中心差分分量边界条件

第19讲角单元系数

第 20 讲 Fortran 代码示例对流问题

第 21 课结果

第22讲其他插值方案

第23课插值方案截断错误

第24讲插值方案的推广

第 25 讲离散化方案的理想性质

第26讲组合对流/扩散问题的稳定性

第 5 节：Navier-Stokes 方程的有限体积法

第27课 Navier-Stokes方程

第28讲 变量的交错网格排列

第29讲压力-速度耦合的简单过程

第 30 讲 X 动量方程的离散化：第 1 部分

第31课 动量方程的欠松弛

第32课 速度校正方程

第33课离散连续性方程

第 34 课交错网格上 Navier-Stokes 求解器（代码）的索引符号

第 35 讲 Navier-Stokes 求解器的 Fortran 代码

第 36 讲 驱动腔和通道问题中的发展流动的描述

第 37 课使用 ParaView 驱动型腔结果

第 38 讲使用 ParaView 的通道流结果

第39讲其他边界条件

第 6 节：差价合约中的错误和不确定性

第 40 讲 CFD 错误和不确定性

高年级本科生和开始研究生水平的工程、数学和科学学生。想要了解 CFD 的工业工程师和科学家。

MP4 | Video: h264, 1280×720 | Audio: AAC, 44.1 KHz
Language: English | Size: 3.09 GB | Duration: 2h 34m

Learn to Write Your Own Codes Using the Finite Volume Method

What you’ll learn
The basics of computational fluid dynamics using the finite volume method.
Requirements
Basic programming skills in a language such as C, Fortran, Python, etc. Knowledge of basic calculus, differential equations, numerical methods, and fluid mechanics is suggested..
Description
This course will cover the basics of the finite volume method for incompressible flows on two-dimensional Cartesian grids. Topics include the discretization procedure, interpolation techniques, boundary conditions, flow visualization using ParaView, and CFD errors and uncertainty. Students will write three codes; the first code solves a pure diffusion problem, the second solves a pure convection problem, and the third solves the Navier-Stokes equations using the SIMPLE pressure-velocity coupling procedure. The Navier-Stokes solver will be used to solve the “driven cavity” problem, and a problem involving the developing flow in a channel. These three codes are also available for download to, for instance, study the solution procedure, or help in debugging a student written code. Upon completion of the course students will be familiar with the basics of the finite volume method, enabling a more effective use of a commercial CFD solver, and possess the background necessary to study more advanced CFD techniques.

Overview

Section 1: Introduction

Lecture 1 A Brief Introduction to CFD and what we will cover in this course.

Lecture 2 Some representative, low-cost CFD results.

Section 2: A review of Finite Difference Approximations and Iterative Methods.

Lecture 3 Derivation of FInite Difference Approximations

Lecture 4 Basic Iterative Solvers

Section 3: Finite Volume Method for Diffusion Problems

Lecture 5 Discretization of Diffusion Terms: Part 1

Lecture 6 Discretization of Diffusion Terms: Part 2

Lecture 7 Discretization of Diffusion Terms: Boundary Conditions

Lecture 8 An Example Problem

Lecture 9 Fortran Code for Example Diffusion Problem

Lecture 10 Section of Fortran Code to Write .csv FIle for ParaView

Lecture 11 Visualization Using ParaView

Section 4: Finite Volume Method for Convection Problems

Lecture 12 Discretization of Convection Terms

Lecture 13 Interpolation Methods: Central “Differencing”

Lecture 14 Interpolation Methods: 1st Order Upwinding

Lecture 15 Deferred Correction to “Blend” Interpolation Schemes

Lecture 16 An Example Problem: Description

Lecture 17 Upwinding Component Boundary Conditions for Example Problem

Lecture 18 Central Differencing Component Boundary Conditions for Example Problem

Lecture 19 Corner Cell Coefficients

Lecture 20 Fortran Code for Example Convection Problem

Lecture 21 Results

Lecture 22 Other Interpolation Schemes

Lecture 23 Interpolation Scheme Truncation Errors

Lecture 24 Generalization of Interpolation Schemes

Lecture 25 Desirable Properties of Discretization Schemes

Lecture 26 Stability of Combined Convection/Diffusion Problems

Section 5: Finite Volume Method for the Navier-Stokes Equations

Lecture 27 The Navier-Stokes Equations

Lecture 28 Staggered Grid Arrangement of Variables

Lecture 29 The SIMPLE Procedure for Pressure-Velocity Coupling

Lecture 30 Discretization of the X-Momentum Equation: Part 1

Lecture 31 Underrelaxation of the Momentum Equations

Lecture 32 The Velocity Correction Equations

Lecture 33 The Discretized Continuity Equation

Lecture 34 Index Notation for Navier-Stokes Solver (Code) on Staggered Grid

Lecture 35 Fortran Code for Navier-Stokes Solver

Lecture 36 Description of Driven Cavity and Developing Flow in a Channel Problems

Lecture 37 Driven Cavity Results Using ParaView

Lecture 38 Channel Flow Results Using ParaView

Lecture 39 Other Boundary Conditions

Section 6: Errors and Uncertainy in CFD

Lecture 40 CFD Errors and Uncertainty

Upper division undergraduate and beginning graduate level engineering, mathematics, and science students. Engineers and scientists working in industry who would like an introduction to CFD.