Does the Matlab 2023a allow to solve 3D partial differential equations?

I need to get a stationary heat field in a 3D object with heat source and convection. Does current Matlab version allow it?

Thanks

[Torsten]

Did you check whether the PDE Toolbox solves the type of equations you want ?

[Fyodor Tatarinov]

I did not find this option in the helper. Older Matlab versions allowed only 2D PDE ( https://www.mathworks.com/matlabcentral/answers/93413-does-the-partial-differential-equation-pde-toolbox-handle-3-dimensional-problems-for-matlab-8-1-r?s_tid=ta_ans_results )

[Torsten]

https://uk.mathworks.com/products/pde.html

You can see from the examples given that in the meantime, the PDE Toolbox also solves general 3d-problems.

And since the heat equation is one of the standard PDEs, I think it is suited to solve the problem you have in mind.

[Fyodor Tatarinov]

I looked in the examples. Most of examples (https://www.mathworks.com/help/pde/examples.html?category=geometry-and-mesh&s_tid=CRUX_topnav) are about importing the geometry from the files, which is not the case, as I need to create it myself.

Really I need a thin cylinder (needle) incerted RADIALLY in a big cylinder down to a certain depth (in the first approximation I can take a cube, assuming that outer cylinder is big enough). There are options as multicuboid and multicylinder, but I did not find the options of shift (there is only Zoffset, but not X- and Y-offset) and rotation, so, as I understood, multicylinder function can create only cylinders with the same axis.

It is also possible to create a meshgrid and then determine a volume inside it by some conditions (as in the example "Sphere in cube" in the helper, but in my case the regular rectangular grid will be either too rough inside th needle or too fine outside, I need a tetraeder grid with changing size, as it is generated in 2D.

[Torsten]

I don't have experience in creating geometries and meshes using the PDE Toolbox, sorry.

Answer 1

[Pavl M.]

Of course OK.

Answer 2

[Ravi Kumar]

Hi Fyodor,

You can create the geometry that you describe in PDE Toolbox. Here is an example. Adjust the dimensions as per your problem:

First create a 2-D geometry with two concentric circles. We will extrude this 2-D geometry to get the desired 3-D shape.

C1 = [1;0;0;0.5];
C2 = [1;0;0;1];
sf = 'C1+C2';
ns = char('C1', 'C2');
gd = [C1,C2];
gm2D = fegeometry(decsg(gd,sf,ns'));
pdegplot(gm2D)

Next, extrude the geometry for two heights to get a stack of concentric cylinders.

gm3D = extrude(gm2D,[0.5,0.5]);
pdegplot(gm3D,'FaceLabels','on')

Then you can extrude only the inner face at the top.

gm3D = extrude(gm3D,6,0.5);
pdegplot(gm3D,'CellLabels','on','FaceAlpha',0.5)

By now, you have the geometry you need. We can do some cleanup to remove unwanted cells using mergeCells() function.

gm3D = mergeCells(gm3D,[1,2]);
pdegplot(gm3D,'CellLabels','on','FaceAlpha',0.5)

gm3D = mergeCells(gm3D,[1,2]);
pdegplot(gm3D,'CellLabels','on','FaceAlpha',0.5)

gm3D = mergeCells(gm3D,[2,3]);
pdegplot(gm3D,'CellLabels','on','FaceAlpha',0.5)

I would also suggest you consider performing an axisymmetric analysis, that would reduce the problem size drastically. Please see this example.

[Torsten]

@Ravi Kumar

Are there tutorials that teach the built-up of easy and more complicated geometries using the PDE Toolbox ? Or does it usually start with imported geometries from CAD tools ?

[Ravi Kumar]

Hi Torsten,

You can import STL and STEP files OR you can use geometry functions to build complicated geometry using primitives as building blocks. You can find some examples on creating complicated geometry starting from primitive shapes.

Few complicated examples:

1. https://www.mathworks.com/help/pde/ug/battery-module-geometry.html
2. https://www.mathworks.com/help/pde/ug/battery-module-cooling-analysis-and-reduced-order-thermal-model.html
3. https://www.mathworks.com/help/pde/ug/electrostatic-analysis-of-transformer-bushing-insulator.html

-Ravi

[Fyodor Tatarinov]

Hi Ravi,

Thank you for your detailed answer. Unfortunately it is not my case, because I have not coaxial, but perpendicular cylinders (really a needle inserted into tree trunc), and I did not find the option to rotate cylinders.