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3D extrusion --QuickField FEA Software -- it offers these modeling modes:
  • Plane-parallel
  • Axisymmetric
  • 3D Extrusion
The modeling is done in 2D in all three cases, and extruded an infinite length in plane-parallel mode and over finite lengths in 3D Extrusion mode, as far as I can tell. For axisymmetric, it is rotated around a line in the modeling plane, sweeping out a 3D shape.

HomePage:Finite Element Method Magnetics -- freeware, does 2D modeling

Ansys | Engineering Simulation Software -- I remember using a 2D-modeling version of Ansoft Maxwell (electromagnetic modeling)
 
If you install it, open the example poblms and pick the heat plate problem theat3.

Click problem view gemottry and yiu will see the mesh. Finet Elements Analysis.Then click on problem-view filed and you get a tempature distrinution across the plate, false color.

Then click view-anaimation.

The general technique is to create an object composed of one or several sections. Each section is given a property, like thermal conductivity.

Edges of the sections are the boundary conditions for solving the PDEs. The technique is not linear meaning you can;t directly apply linear algebra. It s a trial and error method that iterates until relative accuracy limits are reached. It is called a solver.

I don't know exactly how climate is simulated, but the heated plate mesh gives you an idea.

The big thing these tools do is an automatic mesh. Each element has the properties of the section. Then a set of equations are constructed. Then the heat transfer is modeled from each finite elemnt to the other. The geometry of the elements in the mesh are important. They look the way they do for a reason. One is maximizing accuracy. I am not an expert but know the basics.

The technique was known in the 19th century, but it was not practical until computers came along.

Theoretically you could mesh the entire arath and atmospher, and nodel heat trnasfer. The sumulation woud take a very long time.
 
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