Simulation of the heating of two beams

Suppose we want to simulate the heating of four long beams. We can reduce the problem to two dimensions by making a traversal cut. Figure 1 shows a scheme of the problem. The heat supplied is shown as a map of isosurfaces, blue color (lower left corner) being the cooler temperatures, and red color (upper right corner) is the higher temperature.

We can't take advantage of the symmetry of the problem (reducing it to the calculation of one beam), due that the boundary conditions are not symmetric (the heat supplied follows the equation : e2t*sin(x+y)*cosh(x+y) but we can use the geometry of the beams, encapsulating all the behavior of a beam inside a class (called LBeam). This class has information about the domain, the mesh, the equation to be solved and the conditions. The domain is composed of the concatenation of two quadrilaterals, of size 2x1 and 1x1. LBeam objects takes as parameters, the translation (in X and Y) to be applied to the each quadrilateral, and the conductivity coefficients. This class only has a method (the DYNAMIC section), that calls the numeric solver. In this case, we choose the finite element method.

Then, four objects are created. We can parametrize each object with the translation necessary to obtain the configuration of figure 1. The last step is to call the DYNAMIC section of each object, and select the output form.

Figure 1 : Scheme of the Problem

There is also a similar problem, but with moving meshes

Theory pages:
Main page
FEM (i)
FEM (ii)
FDM (i)
Example pages:
1-d Heat Equation
2-d steady state Heat Equation
2-d Heat Equation
1-d non diffusive transport equation
1-d diffusive transport equation
2-d Non diffusive transport equation
Mesh generation with OOCSMP
Moving grids
Application pages:
Heating of two beams
Heating of two moving beams
Solving the equation Ut+Uxx+Uxy+Uyx=0
Solving the equation Ut+Uxx+Uxy+Uyx=0 using MGEN
Heat 1d using several outputs
Solving the Heat equation with a CA
Comparing a CA with the FEM
Gordon's sine equation

Other courses
Other pages

Last modified 22/12/99 by Juan de Lara (, need help for using this courses?.

The OOCSMP code - The SODA code