The problem is time-dependent diffusion with Dirichlet boundary conditions of 0 on the left and 1 on the right. The diffusion coefficient being calculated by the Material is dependent on the average value of a variable on each block. Thus, as the concentration diffuses, the diffusion coefficient increases, but the coefficient is different for each block (based on the average of the variable on that block).

To achieve this we need 3 objects working together:

  1. BlockAverageValue: A UserObject that computes the average value of a variable on each block of the domain and provides averageValue() for retrieving the average value on a particular block.
  2. BlockAverageDiffusionMaterial: A Material that computes "diffusivity" based on the average value of a variable as computed by a BlockAverageValue UserObject.
  3. ExampleDiffusion: The same Kernel we have seen before that uses a "diffusivity" material property. The main purpose of this class is to provide the averageValue method that accepts a SubdomainID, which is simply an integer value specifying which block of the mesh to preform the average value calculation.

Create BlockAverageValue UserObject

The first step is to create a UserObject for computing the average value of a variable on block (subdomain). The complete header and source file for this custom UserObject are linked below, within each file the comments detail the functionality of the class.



Create BlockAverageDiffusionMaterial Material

The second step is to create the Material object that will utilize the block average value for computing a diffusion coefficient. The complete header and source file for this custom Material object are linked below, which includes comments detailing the functionality of the Material. This class simply creates a Material object that creates a material property, "diffusivity", that is computed by the BlockAverageValue class and accessed vial the averageValue method.



Create ExampleDiffusion Kernel

In order to utilize the "diffusivity" material property a Kernel that uses a material property as a coefficient is required. This is accomplished by creating a new Kernel, in this case a Kernel that inherits from the MOOSE Diffusion Kernel. This newly created Kernel simply multiplies the Diffusion Kernel computeQpResidual() and computeQpJacobian() methods with a material property. The complete code for this custom Kernel is supplied in the links below, again the comments in the source detail the behavior of the class.



Running the Problem

Figure 1: Example 20 results after four time steps

Figure 2: Example 20 results after ten time steps

This example may be run using Peacock or by running the following commands form the command line.

cd ~/projects/moose/examples/ex20_user_objects
make -j8
./ex20-opt -i ex20.i

This will generate the results file, ex2_out.e, as shown in Figure 1 and 2. This file may be viewed using Peacock or an external application that supports the Exodus II format (e.g., Paraview).

Complete Input Files