Diffusion Equation

This example solves the weak form of the following diffusion equation,

using the Galerkin Finite Element method. and are the positive definite and symmetric rank two conductivity tensor and a scalar parameter (e.g. thermal capacity) respectively. The dependent variable is a spatially varying scalar field (e.g. temperature). In this example an isotropic and homogeneous material with (identity tensor) and is considered.

Building the example

The fortran version of the example can be configured and built with CMake:

git clone https://github.com/OpenCMISS-Examples/diffusion_equation
cd diffusion_equation
mkdir build
cd build
cmake -DOpenCMISS_INSTALL_ROOT=/path/to/opencmiss/install ../.
make

This will create the example executable "diffusion_equation" in ./src/fortran/ directory.

Running the example

Fortran version:

cd ./src/fortran/
./diffusion_equation

Verifying the example

Results can be visualised by running visualise.cmgui with the Cmgui visualiser.

The following figure shows the finite element mesh (computational domain) and scalar field, (primary variable: e.g. temperature) and its derivative, (secondary variable: e.g. heat flux).

   

Figure 1. (a) Finite element mesh (b) Primary variable solution (c) Secondary variable solution

The expected results from this example are available in expected_results folder.

Prerequisites

There are no additional input files required for this example as it is self-contained.

License

License applicable to this example is described in LICENSE.