GMesh 2.6：有限元素网格划分工具详解与教程

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Gmsh是一款强大的有限元网格生成器，其2.6版本的参考手册提供了详尽的指导，适用于那些希望理解和掌握这一工具的人。这款软件具有内置的预处理和后处理功能，支持用户创建高质量的几何模型并将其转化为可用于数值分析的离散网格。首先，获取Gmsh的方法包括检查官方网站的下载条件，确保遵循版权协议。在使用过程中，该手册分为多个部分，有助于逐步学习： 1. **概述**部分介绍了Gmsh的核心功能，包括几何实体定义（如线、面和体）、有限元素网格的生成，以及与外部求解器的接口，使得用户能够将网格传递给其他数值计算软件进行问题求解。 2. **如何阅读参考手册**提供了导航手册的建议，让读者了解各个章节的结构和内容组织，以便高效地学习和查阅。 3. **运行Gmsh**部分详细讲述了在不同操作系统上安装和启动Gmsh的步骤，确保用户能顺利启动软件并操作界面。 4. **通用工具**涵盖了软件的基本操作，如文件管理、图形交互和基本命令的使用。 5. **几何模块**是关键部分，讲解了如何创建、编辑和修改几何模型，包括多种几何对象的创建方法和高级几何构造技巧。 6. **网格模块**深入解析了网格划分的原理和技术，包括各种网格类型（如三角形、四边形单元等）的选择，以及自适应网格生成算法的介绍。 7. **求解器模块**解释了如何通过Gmsh与外部数值求解器（如FEM、CFD软件）进行集成，以解决实际工程问题。 8. **后处理模块**展示了如何查看和分析生成的网格结果，包括图形输出、数据导出和可视化工具的使用。 9. **文件格式**部分列出了Gmsh支持的输入和输出文件格式，以便用户理解数据交换和兼容性。 10. **教程**为初学者提供了从零开始的步骤指南，通过实践案例帮助他们快速上手。 11. **选项**部分详细解释了软件的各种设置和参数，允许用户根据具体需求调整网格生成过程。 12. **开发者信息**对于软件开发人员或想了解源代码的用户，这部分包含了重要的技术细节和贡献者信息。 13. **常见问题解答**收集了用户可能会遇到的问题及其解决方案，便于快速解决问题。 14. **版本历史**记录了Gmsh的发展历程，显示了软件的稳定性和改进点。 15. **版权和信用**明确了版权归属以及许可使用条款。 16. **许可证**概述了软件使用的开源许可协议，保证了用户的权利和义务。通过阅读这份详细的Gmsh帮助文档，无论是工程师、学生还是科研人员，都能系统地学习和掌握有限元网格划分的关键技能，为数值模拟和工程分析提供强大支持。

6 Gmsh 2.6

prescribes the desired size of the elements in the mesh. This size ﬁeld can be uniform,

speciﬁed by values associated with points in the geometry, or deﬁned by general “ﬁelds”

(for example related to the distance to some boundary, to a arbitrary scalar ﬁeld deﬁned

on another mesh, etc.).

For each meshing step, all structured mesh directives are executed ﬁrst, and serve as addi-

tional constraints for the unstructured parts

1.3 Solver: external solver interface

External solvers can be interfaced with Gmsh through Unix or TCP/IP sockets, which

permits to modify solver parameters, launch external computations and process the results

directly from within Gmsh’s post-processing module. The default solver interfaced with

Gmsh is GetDP (http://geuz.org/getdp/). Examples on how to interface other solvers

are available in the source distribution (in the ‘utils/solvers/’ directory).

1.4 Post-processing: scalar, vector and tensor ﬁeld

visualization

Gmsh can load and manipulate multiple post-processing scalar, vector or tensor maps along

with the geometry and the mesh. Scalar ﬁelds are represented by iso-value lines/surfaces or

color maps, while vector ﬁelds are represented by three-dimensional arrows or displacement

maps. Post-processing functions include section computation, oﬀset, elevation, boundary

and component extraction, color map and range modiﬁcation, animation, vector graphic

output, etc. All the post-processing options can be accessed either interactively or through

the input script ﬁles. Scripting permits to automate all post-processing operations, as for

example to create animations. User-deﬁned operations can also be performed on post-

processing views through dynamically loadable plugins.

1.5 What Gmsh is pretty good at . . .

Here is a tentative list of what Gmsh does best:

• quickly describe simple and/or “repetitive” geometries, thanks to user-deﬁned func-

tions, loops, conditionals and includes (see Section 4.5 [User-deﬁned functions], page 24,

Section 4.6 [Loops and conditionals], page 24, and Section 4.7 [General commands],

page 25);

• parametrize these geometries. Gmsh’s scripting language enables all commands and

command arguments to depend on previous calculations (see Section 4.2 [Expressions],

page 19, and Section 5.1 [Geometry commands], page 31);

• generate 1D, 2D and 3D simplicial (i.e., using line segments, triangles and tetrahedra)

ﬁnite element meshes for CAD models in their native format (without translations)

when linked with the appropriate CAD kernel (see Chapter 6 [Mesh module], page 39);

• specify target element sizes accurately. Gmsh provides several mechanisms to control

the size of the elements in the ﬁnal mesh: through interpolation from sizes speciﬁed at

Note that mixing structured volume grids with unstructured volume grids generated with the default 3D

Delaunay algorithm can result, in certain cases, to non-conform surface meshes on their shared boundary.

If this happens, you may consider using the frontal algorithm for the unstructured part.

Chapter 1: Overview 7

geometry points or using ﬂexible mesh size ﬁelds (see Section 6.3 [Mesh commands],

page 41);

• create simple extruded geometries and meshes (see Section 5.1 [Geometry commands],

page 31, and Section 6.3 [Mesh commands], page 41);

• interact with external solvers through a simple client-server architecture (see Chapter 7

[Solver module], page 59);

• visualize and export computational results in a great variety of ways. Gmsh can display

scalar, vector and tensor datasets, perform various operations on the resulting post-

processing views (see Chapter 8 [Post-processing module], page 61), can export plots

in many diﬀerent formats (see Section B.1 [General options list], page 129), and can

generate complex animations (see Chapter 4 [General tools], page 19, and Section A.8

[t8.geo], page 116);

• run on low end machines and/or machines with no graphical interface. Gmsh can be

compiled with or without the GUI, and all versions can be used either interactively

or directly from the command line (see Chapter 3 [Running Gmsh on your system],

page 11);

• conﬁgure your preferred options. Gmsh has a large number of conﬁguration options

that can be set interactively using the GUI, scattered inside command ﬁles, changed on

the ﬂy in scripts, set in per-user conﬁguration ﬁles, or speciﬁed on the command-line

(see Chapter 3 [Running Gmsh on your system], page 11 and Appendix B [Options],

page 129);

• and do all the above on various platforms (Windows, Mac and Unix), for free (see

[Copying conditions], page 3), using simple script ﬁles and/or a small but powerful

GUI.

1.6 . . . and what Gmsh is not so good at

As of version 2.6, here are some known weaknesses of Gmsh:

• the BRep approach for describing geometries can become inconvenient/ineﬃcient for

large models. For complex models, or if you want to use a solid-modeler approach,

you should link Gmsh with an external CAD kernel and import native ﬁles directly.

(The binary versions available on http://geuz.org/gmsh/ are linked with the free

CAD kernel OpenCASCADE, which enables native BREP import as well as STEP

and IGES import.)

• Gmsh is not a multi-bloc generator: all meshes produced by Gmsh are conforming in

the sense of ﬁnite element meshes;

• Gmsh’s user interface is only exposing a limited number of the available features, and

many aspects of the interface could be enhanced (especially manipulators).

• Gmsh’s scripting language is fairly limited, providing only very crude loop controls and

user-deﬁned functions, with no local variables.

• there is no global “undo” capability. You will often need to edit a text ﬁle to correct

mistakes.

If you have the skills and some free time, feel free to join the project: we gladly accept any

code contributions (see Appendix C [Information for developers], page 193) to remedy the

aforementioned (and all other) shortcomings!

Chapter 2: How to read this reference manual? 9

2 How to read this reference manual?

Gmsh can be used at three levels:

1. as a stand-alone graphical program, driven by an interactive graphical user interface

(GUI);

2. as a stand-alone script-driven program;

3. as a library.

You can skip most of this reference manual if you only want to use Gmsh at the ﬁrst

level (i.e., interactively with the GUI). Just read the next chapter (see Chapter 3 [Run-

ning Gmsh on your system], page 11) to learn how to launch Gmsh on your system, then

go experiment with the GUI and the tutorial ﬁles (see Appendix A [Tutorial], page 103)

provided in the distribution. Screencasts that show how to use the GUI are available here:

http://geuz.org/gmsh/screencasts/.

The aim of the reference manual is to explain everything you need to use Gmsh at the

second level, i.e., using the built-in scripting language. A Gmsh script ﬁle is an ASCII

text ﬁle that contains instructions in Gmsh’s built-in scripting language. Such a ﬁle is

interpreted by Gmsh’s parser, and can be given any extension (or no extension at all). By

convention, Gmsh uses the ‘.geo’ extension for geometry scripts, and the ‘.pos’ extension

for parsed post-processing datasets. Once you master the tutorial (read the source ﬁles:

they are heavily commented!), start reading chapter Chapter 4 [General tools], page 19,

then proceed with the next four chapters, which detail the syntax of the geometry, mesh,

solver and post-processing scripting commands. You will see that most of the interactive

actions in the GUI have a direct equivalent in the scripting language. If you want to use

Gmsh as a pre- or post-processor for your own software, you will also want to learn about

the non-scripting input/output ﬁles that Gmsh can read/write. In addition to Gmsh’s

native “MSH” ﬁle format (see Chapter 9 [File formats], page 87), Gmsh can read/write

many standard mesh ﬁles, depending on how it was built: check the ‘File->Save As’ menu

for a list of available formats.

Finally, to use Gmsh at the third level (i.e., to link the Gmsh library with your own code),

you will need to learn the internal Gmsh Application Programming Interface (API). No

complete documentation of this API is available yet; a good starting point is Section C.2

[Source code structure], page 193, which gives a short introduction to Gmsh’s internal source

code structure. Then have a look e.g. at the examples in the ‘utils/api_demos/’ directory

in the source code. Due to the many possible conﬁguration options (and associated external

dependencies), we currently do not distibute precompiled versions of the Gmsh library.

To build the library see the instructions in the top-level ‘README.txt’ ﬁle in the source

distribution.

2.1 Syntactic rules used in the manual

Here are the rules we tried to follow when writing this reference manual. Note that meta-

syntactic variable deﬁnitions stay valid throughout the manual (and not only in the sections

where the deﬁnitions appear).

1. Keywords and literal symbols are printed like this.

2. Metasyntactic variables (i.e., text bits that are not part of the syntax, but stand for

other text bits) are printed like this.

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