Merge pull request #187 from yiyuef/master

Adding a new tutorial (Advection-Deffusion Equation)

Author: JordiManyer

assets/advection_diffusion/Pentagon_2D_Mesh.png

@@ -14,6 +14,7 @@ files = [
   "Darcy equation (with RT)"=>"darcy.jl",
   "Incompressible Navier-Stokes"=>"inc_navier_stokes.jl",
   "Stokes equation" => "stokes.jl",
+  "Advection-diffusion" => "advection_diffusion.jl",
   "Isotropic damage model" => "isotropic_damage.jl",
   "Fluid-Structure Interaction"=>"fsi_tutorial.jl",
   "Electromagnetic scattering in 2D"=>"emscatter.jl",

assets/advection_diffusion/Result_non_zero.png

@@ -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.