CFD入门指南：理论、数值方法与开源应用解析

需积分: 0 57 浏览量更新于2024-06-14 收藏 17.7MB PDF 举报

"《计算流体力学（CFD）领域，基本理论，数值方法，典型应用》是一本经典的CFD教材，适用于本科和研究生学习，强调开源软件的应用，适合初学者和开发者。" 本书深入探讨了计算流体力学的基础知识，主要分为三个核心部分： 1. 理论推导：这部分内容涵盖流体力学的基本原理，如纳维-斯托克斯方程（Navier-Stokes equations）和连续性方程，这些是描述流体运动的基本数学模型。它还会讲解理想流体与粘性流体的区别，以及如何在不同边界条件下应用这些方程。此外，还会涉及流体动力学中的守恒定律，如质量、动量和能量守恒。 2. 数值计算方法：在这一章节，作者将介绍用于求解流体动力学方程的各种数值方法，如有限差分法、有限体积法和有限元法。读者将学习到如何离散化连续方程，构建并求解离散系统。此外，还将讨论稳定性分析和误差分析，以理解数值方法的精度和收敛性。网格生成技术，如结构化和非结构化网格，也是这一部分的重要内容。 3. 典型应用场景：书中会展示CFD在实际问题中的应用，如航空航天中的气动布局优化、汽车工业中的流场分析、环境工程中的污染扩散模拟、生物医学工程中的血液流动研究等。这些案例不仅有助于理解理论知识，还帮助读者掌握如何使用开源CFD软件，如OpenFOAM、CFD++或FreeFOAM，进行实际计算和结果后处理。书中的"An Open Source Approach"强调了使用开源软件进行教学和研究的重要性。作者Brian C. Vermeire、Carlos A. Pereira和Hamidreza Karbasian通过开放教育资源（OER）项目，使得这本教材可以免费获取，鼓励学术界和工业界的共享和协作。采用 Creative Commons Attribution-NonCommercial 3.0 Unported License，允许读者在遵循特定许可条款的情况下自由使用和分享内容，但不应用于商业目的。本书的第一版发布于2020年10月，其前言揭示了这本书的起源，源自作者在康考迪亚大学教授的本科生和研究生计算流体力学课程。通过这种方式，作者希望为学生和研究者提供一个免费且实用的学习资源，推动CFD领域的知识传播和创新。

16 Chapter 2. The Navier Stokes Equations

The ﬁrst of the surface forces is due to the pressure surrounding the system. Since pressure acts

normal to a surface, the total pressure force

can be obtained via integration along the surface.

Hence,

−pˆnds, (2.5)

where

is the pressure and the negative is included since pressure exerts a force inwards, but

our normal vector is deﬁned as outwards. The second set of surface terms is due to the effects of

viscosity. To account for these we introduce the Cauchy stress tensor

, which for Newtonian ﬂuids

is [7]

τ = µ



∇~v + (∇~v)



−

µ (∇ ·~v)I, (2.6)

where

is the dynamic viscosity and

is an identity matrix. Whereas pressure acts normal to the

control volume surface, viscous effects act parallel to it. Hence, the total viscous force

can be

obtained via integration

τ · ˆnds. (2.7)

With the inviscid and viscous forces determined, conservation of momentum can be written as

Ω

ρ~vd~x+

ρ~v(~v· ˆn)ds =

−Pˆnds +

τ · ˆnds, (2.8)

which is commonly written by grouping all of the surface integral terms

Ω

ρ~vd~x+

[ρ~v⊗~v−σ ] · ˆnds = 0, (2.9)

where

σ = −pI + τ. (2.10)

2.1.3 Conservation of Energy

From conservation of energy, the rate of change of energy within the system is equal to the rate of

heat added to the system less the rate work done by the system on its surroundings. Hence,

Q−

W, (2.11)

where

is the energy in the system,

is heat rate, and

is work rate. In this case, the energy per

unit volume is ρe where

e = c

T +

~v·~v, (2.12)

is the speciﬁc energy,

is the speciﬁc heat at constant volume, and

is the temperature. Using

Reynolds transport theorem, we have

Ω

ρed~x+

ρe(~v · ˆn)ds =

Q−

W. (2.13)

Since body forces have been neglected, the work done by the system on its surroundings is due

to only surface forces. The work done by pressure

is due to the product of the pressure force,

18 Chapter 2. The Navier Stokes Equations

Ω

~wd~x +

inv

−

vis

· ˆnds = 0. (2.23)

2.2 Divergence Form

Looking back at the previous section, we note that Equation 1.2 is a general conservation law for

a ﬁnite control volume. In some contexts, speciﬁcally when using the ﬁnite-volume method that

will be introduced later, this integral form of the governing equations is used. However, other

approaches in CFD use a nearly equivalent divergence form of Equation 1.2. To derive this form,

we rely on the divergence theorem, also known as Gauss theorem.

Theorem 2.2.1 — Divergence Theorem.

The divergence theorem states that integrals of the

following form are equivalent for a continuously differentiable vector ﬁeld

Ω

∇ ·

Fd~x =

F · ˆnds, (2.24)

which allows us to transform volume integrals into surface integrals, or the reverse.

2.2.1 Conservation of Mass

Starting from the integral form of conservation of mass and applying the divergence theorem to the

surface term, we obtain

Ω

ρd~x +

Ω

∇ ·(ρ~v)d~x = 0. (2.25)

Since integration and differentiation commute, we can bring the time derivative inside of the ﬁrst

integral

Ω

∂ ρ

∂t

d~x +

Ω

∇ ·(ρ~v)d~x = 0. (2.26)

and noticing that the bounds of both integrals are the same

Ω



∂ ρ

∂t

+ ∇ ·(ρ~v)



d~x = 0. (2.27)

In order for this equation to be valid, other than in trivial cases, we require that the integrand be

identically zero. Hence, conservation of mass in divergence form can be written as

∂ ρ

∂t

+ ∇ ·(ρ~v) = 0. (2.28)

It is interesting to note that we have effectively converted a problem involving surface and volume

integrals, into a differential form that requires computing derivatives.

A subtle difference between the two forms of conservation laws is that the integral form

applies to control volumes and the divergence form applies at points. This will become

important in choosing what form to use for CFD, and will be explored later.

2.2.2 Conservation of Momentum

Applying the same sets of operations to the integral form of the momentum equation, we can obtain

its divergence form

剩余214页未读，继续阅读

猿核试Bug愁

粉丝: 2374
资源: 26

CFD入门指南：理论、数值方法与开源应用解析

计算流体力学基础（CFD）

计算流体力学基础 与CFD软件应用

流体力学与CFD基础.

计算流体力学 经典教材

计算流体力学作业-平板上的超声速流动的数值求解

计算流体力学及其并行算法

计算流体力学各种程序.rar

CFD软件及源程序辅助工程流体力学课程教学的探索与实践.docx

理论与应用力学专业计算力学课后作业汇总

FLUENT实用工具宏详解：数值计算方法与工程应用

最新资源

计算流体力学基础与CFD软件应用

计算流体力学经典教材