如何在Gmsh中为中间细化层生成结构化交替3D网格？

安全阿岳

2026-7-20

Gmsh中间结构化细化层箱体网格实现方案

我尝试在Gmsh中创建带有中间结构化细化层的箱体网格，当前2D网格符合预期，但生成3D网格时中间层元素变为对角元，需要实现中间层的结构化交替3D网格。以下是初始.geo代码：

lc = 100.;
Mesh.CharacteristicLengthFromPoints = 1.;
Mesh.CharacteristicLengthExtendFromBoundary = 1.;
Mesh.CharacteristicLengthFromCurvature = 1.;
Mesh.CharacteristicLengthMin = 10.;
Mesh.CharacteristicLengthMax = lc;

Lbox = 100;
Hbox = 100;
Wbox = 100;

Wref = 12;

Point(1) = {0, 0, (Wbox - Wref)/2, 1.0};
Point(2) = {Lbox, 0, (Wbox - Wref)/2, 1.0};
Point(3) = {Lbox, Hbox, (Wbox - Wref)/2, 1.0};
Point(4) = {0, Hbox, (Wbox - Wref)/2, 1.0};

Line(1) = {2, 1};
Line(2) = {1, 4};
Line(3) = {4, 3};
Line(4) = {3, 2};
Curve Loop(1) = {4, 1, 2, 3};
Plane Surface(1) = {1};

size_el = 1.5;
n_el_big = Lbox/size_el + 1.;
n_el_small = Wref/size_el + 1.;

Extrude {0, 0, Wref} {
  Surface{1}; //Layers{n_el_small};
}

Transfinite Curve {2, 3, 4, 1, 8, 9, 6, 7} = n_el_big Using Progression 1;
Transfinite Curve {20, 11, 12, 16} = n_el_small Using Progression 1;
Transfinite Surface {1} Alternate;
Transfinite Surface {21} Alternate;
Transfinite Surface {26} Alternate;
Transfinite Surface {13} Alternate;
Transfinite Surface {25} Alternate;
Transfinite Surface {17} Alternate;

/*//Recombine Surface {1, 21, 26, 13, 25, 17}; Used to have hexahedron elements*/

Transfinite Volume{1} = {14, 10, 6, 5, 4, 1, 2, 3};


Point(15) = {0, 0, 0, 1.0};
Point(16) = {Lbox, 0, 0, 1.0};
Point(17) = {Lbox, Hbox, 0, 1.0};
Point(18) = {0, Hbox, 0, 1.0};
Point(19) = {0, 0, Wbox, 1.0};
Point(20) = {Lbox, 0, Wbox, 1.0};
Point(21) = {Lbox, Hbox, Wbox, 1.0};
Point(22) = {0, Hbox, Wbox, 1.0};
Line(21) = {14, 22};
Line(22) = {22, 21};
Line(23) = {21, 5};
Line(24) = {22, 19};
Line(25) = {19, 10};
Line(26) = {19, 20};
Line(27) = {20, 6};
Line(28) = {20, 21};
Line(29) = {2, 16};
Line(30) = {16, 17};
Line(31) = {17, 3};
Line(32) = {17, 18};
Line(33) = {18, 4};
Line(34) = {18, 15};
Line(35) = {15, 1};
Line(36) = {15, 16};


/*//+*/
Curve Loop(2) = {31, -3, -33, -32};
Plane Surface(27) = {2};
Curve Loop(3) = {33, -2, -35, -34};
Plane Surface(28) = {3};
Curve Loop(4) = {35, -1, 29, -36};
Plane Surface(29) = {4};
Curve Loop(5) = {30, 31, 4, 29};
Plane Surface(30) = {5};
Curve Loop(6) = {32, 34, 36, 30};
Plane Surface(31) = {6};
Curve Loop(7) = {23, 6, -27, 28};
Plane Surface(32) = {7};
Curve Loop(8) = {23, -9, 21, 22};
Plane Surface(33) = {8};
Curve Loop(9) = {27, 7, -25, 26};
Plane Surface(34) = {9};
Curve Loop(10) = {25, 8, 21, 24};
Plane Surface(35) = {10};
Curve Loop(11) = {26, 28, -22, 24};
Plane Surface(36) = {11};
Surface Loop(1) = {35, 34, 32, 33, 36, 26};
Volume(2) = {1};
Surface Loop(2) = {28, 27, 30, 31, 29, 1};
Volume(3) = {2};


Transfinite Curve {33, 35, 25, 31, 27, 23} = 6 Using Progression 0.6;
Transfinite Curve {29, 21} = 6 Using Progression 1.4;

问题原因及解决步骤

Extrude未指定Layers：拉伸中间层时未明确层数，导致网格节点数不匹配，需启用Layers{n_el_small}参数
未重组曲面：注释掉了曲面重组命令，结构化四边形曲面是生成六面体网格的前提，必须启用Recombine Surface
Transfinite Volume缺失Alternate关键字：未指定体的交替结构，导致生成对角元
未重组体：需对中间层Volume执行重组，强制生成六面体元素

修改后的核心代码片段

// 修正Extrude，指定拉伸层数
Extrude {0, 0, Wref} {
  Surface{1}; Layers{n_el_small};
}

// 启用曲面重组，生成结构化四边形
Recombine Surface {1, 21, 26, 13, 25, 17};

// 修正Transfinite Volume，添加Alternate关键字
Transfinite Volume{1} = {14, 10, 6, 5, 4, 1, 2, 3} Alternate;

// 重组中间层Volume，生成六面体元素
Recombine Volume {1};

完整修改后代码

lc = 100.;
Mesh.CharacteristicLengthFromPoints = 1.;
Mesh.CharacteristicLengthExtendFromBoundary = 1.;
Mesh.CharacteristicLengthFromCurvature = 1.;
Mesh.CharacteristicLengthMin = 10.;
Mesh.CharacteristicLengthMax = lc;

Lbox = 100;
Hbox = 100;
Wbox = 100;

Wref = 12;

Point(1) = {0, 0, (Wbox - Wref)/2, 1.0};
Point(2) = {Lbox, 0, (Wbox - Wref)/2, 1.0};
Point(3) = {Lbox, Hbox, (Wbox - Wref)/2, 1.0};
Point(4) = {0, Hbox, (Wbox - Wref)/2, 1.0};

Line(1) = {2, 1};
Line(2) = {1, 4};
Line(3) = {4, 3};
Line(4) = {3, 2};
Curve Loop(1) = {4, 1, 2, 3};
Plane Surface(1) = {1};

size_el = 1.5;
n_el_big = Lbox/size_el + 1.;
n_el_small = Wref/size_el + 1.;

// 启用Layers参数，明确拉伸层数
Extrude {0, 0, Wref} {
  Surface{1}; Layers{n_el_small};
}

Transfinite Curve {2, 3, 4, 1, 8, 9, 6, 7} = n_el_big Using Progression 1;
Transfinite Curve {20, 11, 12, 16} = n_el_small Using Progression 1;
Transfinite Surface {1} Alternate;
Transfinite Surface {21} Alternate;
Transfinite Surface {26} Alternate;
Transfinite Surface {13} Alternate;
Transfinite Surface {25} Alternate;
Transfinite Surface {17} Alternate;

// 重组曲面，生成结构化四边形网格
Recombine Surface {1, 21, 26, 13, 25, 17};

// 添加Alternate关键字，指定体的交替结构
Transfinite Volume{1} = {14, 10, 6, 5, 4, 1, 2, 3} Alternate;

// 重组体，强制生成六面体元素
Recombine Volume {1};


Point(15) = {0, 0, 0, 1.0};
Point(16) = {Lbox, 0, 0, 1.0};
Point(17) = {Lbox, Hbox, 0, 1.0};
Point(18) = {0, Hbox, 0, 1.0};
Point(19) = {0, 0, Wbox, 1.0};
Point(20) = {Lbox, 0, Wbox, 1.0};
Point(21) = {Lbox, Hbox, Wbox, 1.0};
Point(22) = {0, Hbox, Wbox, 1.0};
Line(21) = {14, 22};
Line(22) = {22, 21};
Line(23) = {21, 5};
Line(24) = {22, 19};
Line(25) = {19, 10};
Line(26) = {19, 20};
Line(27) = {20, 6};
Line(28) = {20, 21};
Line(29) = {2, 16};
Line(30) = {16, 17};
Line(31) = {17, 3};
Line(32) = {17, 18};
Line(33) = {18, 4};
Line(34) = {18, 15};
Line(35) = {15, 1};
Line(36) = {15, 16};


/*//+*/
Curve Loop(2) = {31, -3, -33, -32};
Plane Surface(27) = {2};
Curve Loop(3) = {33, -2, -35, -34};
Plane Surface(28) = {3};
Curve Loop(4) = {35, -1, 29, -36};
Plane Surface(29) = {4};
Curve Loop(5) = {30, 31, 4, 29};
Plane Surface(30) = {5};
Curve Loop(6) = {32, 34, 36, 30};
Plane Surface(31) = {6};
Curve Loop(7) = {23, 6, -27, 28};
Plane Surface(32) = {7};
Curve Loop(8) = {23, -9, 21, 22};
Plane Surface(33) = {8};
Curve Loop(9) = {27, 7, -25, 26};
Plane Surface(34) = {9};
Curve Loop(10) = {25, 8, 21, 24};
Plane Surface(35) = {10};
Curve Loop(11) = {26, 28, -22, 24};
Plane Surface(36) = {11};
Surface Loop(1) = {35, 34, 32, 33, 36, 26};
Volume(2) = {1};
Surface Loop(2) = {28, 27, 30, 31, 29, 1};
Volume(3) = {2};


Transfinite Curve {33, 35, 25, 31, 27, 23} = 6 Using Progression 0.6;
Transfinite Curve {29, 21} = 6 Using Progression 1.4;

验证说明

修改后生成的中间层3D网格会是结构化交替的六面体元素，而非对角元。关键在于确保曲面重组为四边形，体的Transfinite设置包含Alternate关键字，同时重组体元素。

内容的提问来源于stack exchange，提问作者Gabriel Dante

如何在Gmsh中为中间细化层生成结构化交替3D网格？

问题原因及解决步骤 #

修改后的核心代码片段 #

完整修改后代码 #

验证说明 #

问题原因及解决步骤

修改后的核心代码片段

完整修改后代码

验证说明