diff --git a/assets/advection_diffusion/Pentagon.geo b/assets/advection_diffusion/Pentagon.geo new file mode 100644 index 0000000..9dedf49 --- /dev/null +++ b/assets/advection_diffusion/Pentagon.geo @@ -0,0 +1,156 @@ +// Gmsh project created on Wed Dec 4 14:27:19 2024 +// ----------------------------------------------------------------------------- +// +// Gmsh GEO tutorial 1 +// +// Geometry basics, elementary entities, physical groups +// +// ----------------------------------------------------------------------------- + +// The simplest construction in Gmsh's scripting language is the +// `affectation'. The following command defines a new variable `lc': + +lc = 1e-1; + +// This variable can then be used in the definition of Gmsh's simplest +// `elementary entity', a `Point'. A Point is uniquely identified by a tag (a +// strictly positive integer; here `1') and defined by a list of four numbers: +// three coordinates (X, Y and Z) and the target mesh size (lc) close to the +// point: + + + +// The distribution of the mesh element sizes will then be obtained by +// interpolation of these mesh sizes throughout the geometry. Another method to +// specify mesh sizes is to use general mesh size Fields (see `t10.geo'). A +// particular case is the use of a background mesh (see `t7.geo'). + +// If no target mesh size of provided, a default uniform coarse size will be +// used for the model, based on the overall model size. + +// We can then define some additional points. All points should have different +// tags: + +Point(1) = {0, -1.0000, 0, lc}; +Point(2) = {0, 1.0000, 0, lc}; +Point(3) = {1.9015, 1.6190, 0, lc}; +Point(4) = {3.0777, 0, 0, lc}; +Point(5) = {1.9015, -1.6190, 0, lc}; + +// Point(1) = {0.8507, 0, 0, lc}; +// Point(2) = {0.2629, 0.8090, 0, lc}; +// Point(3) = {-0.6882, 0.5000, 0, lc}; +// Point(4) = {-0.6882, -0.5000, 0, lc}; +// Point(5) = {0.2629, -0.8090, 0, lc}; + +// Curves are Gmsh's second type of elementary entities, and, amongst curves, +// straight lines are the simplest. A straight line is identified by a tag and +// is defined by a list of two point tags. In the commands below, for example, +// the line 1 starts at point 1 and ends at point 2. +// +// Note that curve tags are separate from point tags - hence we can reuse tag +// `1' for our first curve. And as a general rule, elementary entity tags in +// Gmsh have to be unique per geometrical dimension. + +Line(1) = {1, 2}; +Line(2) = {2, 3}; +Line(3) = {3, 4}; +Line(4) = {4, 5}; +Line(5) = {5, 1}; + +// The third elementary entity is the surface. In order to define a simple +// rectangular surface from the four curves defined above, a curve loop has +// first to be defined. A curve loop is also identified by a tag (unique amongst +// curve loops) and defined by an ordered list of connected curves, a sign being +// associated with each curve (depending on the orientation of the curve to form +// a loop): + +Curve Loop(1) = {1, 2, 3, 4, 5}; + +// We can then define the surface as a list of curve loops (only one here, +// representing the external contour, since there are no holes--see `t4.geo' for +// an example of a surface with a hole): + +Plane Surface(1) = {1}; + +// At this level, Gmsh knows everything to display the rectangular surface 1 and +// to mesh it. An optional step is needed if we want to group elementary +// geometrical entities into more meaningful groups, e.g. to define some +// mathematical ("domain", "boundary"), functional ("left wing", "fuselage") or +// material ("steel", "carbon") properties. +// +// Such groups are called "Physical Groups" in Gmsh. By default, if physical +// groups are defined, Gmsh will export in output files only mesh elements that +// belong to at least one physical group. (To force Gmsh to save all elements, +// whether they belong to physical groups or not, set `Mesh.SaveAll=1;', or +// specify `-save_all' on the command line.) Physical groups are also identified +// by tags, i.e. strictly positive integers, that should be unique per dimension +// (0D, 1D, 2D or 3D). Physical groups can also be given names. +// +// Here we define a physical curve that groups the left, bottom and right curves +// in a single group (with prescribed tag 5); and a physical surface with name +// "My surface" (with an automatic tag) containing the geometrical surface 1: + +Physical Line("l1") = {1}; +Physical Line("l2") = {2}; +Physical Line("l3") = {3}; +Physical Line("l4") = {4}; +Physical Line("l5") = {5}; + +Physical Curve(“b1”) = {1, 2, 4}; +Physical Curve("b2") = {3}; + +Physical Surface("My surface") = {1}; + +// Now that the geometry is complete, you can +// - either open this file with Gmsh and select `2D' in the `Mesh' module to +// create a mesh; then select `Save' to save it to disk in the default format +// (or use `File->Export' to export in other formats); +// - or run `gmsh t1.geo -2` to mesh in batch mode on the command line. + +// You could also uncomment the following lines in this script: +// +Mesh 2; +Save "pentagon_mesh.msh"; +// +// which would lead Gmsh to mesh and save the mesh every time the file is +// parsed. (To simply parse the file from the command line, you can use `gmsh +// t1.geo -') + +// By default, Gmsh saves meshes in the latest version of the Gmsh mesh file +// format (the `MSH' format). You can save meshes in other mesh formats by +// specifying a filename with a different extension in the GUI, on the command +// line or in scripts. For example +// +// Save "t1.unv"; +// +// will save the mesh in the UNV format. You can also save the mesh in older +// versions of the MSH format: +// +// - In the GUI: open `File->Export', enter your `filename.msh' and then pick +// the version in the dropdown menu. +// - On the command line: use the `-format' option (e.g. `gmsh file.geo -format +// msh2 -2'). +// - In a `.geo' script: add `Mesh.MshFileVersion = x.y;' for any version +// number `x.y'. +// - As an alternative method, you can also not specify the format explicitly, +// and just choose a filename with the `.msh2' or `.msh4' extension. + +// Note that starting with Gmsh 3.0, models can be built using other geometry +// kernels than the default built-in kernel. By specifying +// +// SetFactory("OpenCASCADE"); +// +// any subsequent command in the `.geo' file would be handled by the OpenCASCADE +// geometry kernel instead of the built-in kernel. Different geometry kernels +// have different features. With OpenCASCADE, instead of defining the surface by +// successively defining 4 points, 4 curves and 1 curve loop, one can define the +// rectangular surface directly with +// +// Rectangle(2) = {.2, 0, 0, .1, .3}; +// +// The underlying curves and points could be accessed with the `Boundary' or +// `CombinedBoundary' operators. +// +// See e.g. `t16.geo', `t18.geo', `t19.geo' or `t20.geo' for complete examples +// based on OpenCASCADE, and `examples/boolean' for more. \ No newline at end of file diff --git a/assets/advection_diffusion/Pentagon_2D_Mesh.png b/assets/advection_diffusion/Pentagon_2D_Mesh.png new file mode 100644 index 0000000..bd7b10a Binary files /dev/null and b/assets/advection_diffusion/Pentagon_2D_Mesh.png differ diff --git a/assets/advection_diffusion/Result_non_zero.png b/assets/advection_diffusion/Result_non_zero.png new file mode 100644 index 0000000..5e8ccce Binary files /dev/null and b/assets/advection_diffusion/Result_non_zero.png differ diff --git a/assets/advection_diffusion/Result_zero.png b/assets/advection_diffusion/Result_zero.png new file mode 100644 index 0000000..2bf5c22 Binary files /dev/null and b/assets/advection_diffusion/Result_zero.png differ diff --git a/assets/advection_diffusion/pentagon_mesh.msh b/assets/advection_diffusion/pentagon_mesh.msh new file mode 100644 index 0000000..a2667f3 --- /dev/null +++ b/assets/advection_diffusion/pentagon_mesh.msh @@ -0,0 +1,3644 @@ +$MeshFormat +4.1 0 8 +$EndMeshFormat +$PhysicalNames +7 +1 1 "l1" +1 2 "l2" +1 3 "l3" +1 4 "l4" +1 5 "l5" +1 6 "b2" +2 7 "My surface" +$EndPhysicalNames +$Entities +5 5 1 0 +1 0 -1 0 0 +2 0 1 0 0 +3 1.9015 1.619 0 0 +4 3.0777 0 0 0 +5 1.9015 -1.619 0 0 +1 0 -1 0 0 1 0 1 1 2 1 -2 +2 0 1 0 1.9015 1.619 0 1 2 2 2 -3 +3 1.9015 0 0 3.0777 1.619 0 2 3 6 2 3 -4 +4 1.9015 -1.619 0 3.0777 0 0 1 4 2 4 -5 +5 0 -1.619 0 1.9015 -1 0 1 5 2 5 -1 +1 0 -1.619 0 3.0777 1.619 0 1 7 5 1 2 3 4 5 +$EndEntities +$Nodes +11 899 1 899 +0 1 0 1 +1 +0 -1 0 +0 2 0 1 +2 +0 1 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