如何用Gmsh生成近乎结构化的指定边长二维四边形网格？

Absolutely, you can get that clean quasi-structured quad mesh you're targeting in Gmsh—you just need to move beyond the default free meshing mode and use Gmsh's structured meshing tools. Here's how to tweak your script to make it happen:

Key Fixes for Your Gmsh Script #

The core issue with your original code is that it relies on Gmsh's automatic free mesher, which defaults to unstructured grids for complex geometries. Instead, use transfinite meshing to enforce structured grids where possible, with only local deformation around your hole.

Here's the revised script with explanations:

lc = 1;

# Outer rectangle geometry (fixed line order for consistency)
Point(1) = {0, 0, 0, lc};
Point(2) = {10, 0, 0, lc};
Point(3) = {10, 4, 0, lc};
Point(4) = {0, 4, 0, lc};
Line(1) = {1,2};
Line(2) = {2,3};
Line(3) = {3,4};
Line(4) = {4,1};

# Inner triangular hole (adjusted line loop direction)
Point(5) = {1, 1, 0, lc};
Point(6) = {3, 1, 0, lc};
Point(7) = {2, 2, 0, lc};
Line(5) = {5,6};
Line(6) = {6,7};
Line(7) = {7,5};

# Define line loops and surface (ensure outer loop is counter-clockwise, inner is clockwise)
Line Loop(1) = {1,2,3,4};
Line Loop(2) = {-5,-6,-7};  # Negative signs reverse line direction for correct hole definition
Plane Surface(1) = {1,2};

# --- Critical for quasi-structured quads ---
# Set transfinite lines to enforce uniform node spacing
Transfinite Line{1,3} = 11 Using Progression 1;  # 10 units / 1 lc = 11 nodes (even spacing)
Transfinite Line{2,4} = 5 Using Progression 1;   # 4 units / 1 lc = 5 nodes
Transfinite Line{5} = 3 Using Progression 1;     # Match outer mesh density along the hole's bottom edge
Transfinite Line{6,7} = 2 Using Progression 1;   # Adjust for diagonal edges to minimize distortion

# Generate structured surface mesh and force quadrilaterals
Transfinite Surface{1};
Recombine Surface{1};

# Optional: Smooth local distortion around the hole
Mesh.Optimize = 1;
Mesh.OptimizeNetgen = 1;

What Each Part Does: #

• Transfinite Lines: Tells Gmsh to place nodes evenly along each edge, creating the foundation for a structured grid. You can either specify node counts manually (like above) or let Gmsh calculate them from lc.
• Transfinite Surface: Maps the edge nodes to the entire surface, producing a structured quad grid that only deforms locally around the hole.
• Recombine Surface: Ensures no triangular elements are generated—all cells stay quadrilateral.
• Mesh Optimization: Reduces minor distortions around the hole to make the local mesh smoother.

Alternative Open-Source Tools #

If you prefer a GUI or simpler workflow, these tools can also generate quasi-structured quad meshes:

• Netgen: Its 2D meshing engine is designed for this kind of geometry, with built-in support for structured grids around holes. It integrates seamlessly with Gmsh too.
• FreeCAD: Has a built-in mesh workbench that uses both Gmsh and Netgen. You can define your geometry visually, then select "structured quad" meshing options for clean results.

内容的提问来源于stack exchange，提问作者Unis