Iron-Water¶

Git reference: Example neutronics-iron-water.

This example is very similar to the example “saphir”, the main difference being that it reads a mesh file in the exodusii format (created by Cubit). This example only builds if you have the ExodusII and NetCDF libraries installed on your system and the variables WITH_EXODUSII, EXODUSII_ROOT and NETCDF_ROOT defined properly. The latter can be done, for example, in the CMake.vars file as follows:

SET(WITH_EXODUSII YES)
SET(EXODUSII_ROOT /opt/packages/exodusii)
SET(NETCDF_ROOT   /opt/packages/netcdf)

The mesh is now loaded using the ExodusIIReader (see the mesh_loader.h file):

// Load the mesh
Mesh mesh;
ExodusIIReader mloader;
if (!mloader.load("iron-water.e", &mesh)) error("ExodusII mesh load failed.");

The model describes an external-force-driven configuration without fissile materials present. We will solve the one-group neutron diffusion equation

(1)-\nabla \cdot (D(x,y) \nabla \Phi) + \Sigma_a(x,y) \Phi = Q_{ext}(x,y).

The domain of interest is a 30 x 30 cm square consisting of four regions. A uniform volumetric source is placed in water in the lower-left corner of the domain, surrounded with a layer of water, a layer of iron, and finally another layer of water:

Schematic picture for the iron-water example.

The unknown is the neutron flux \Phi(x, y). The values of the diffusion coefficient D(x, y), absorption cross-section \Sigma_a(x, y) and the source term Q_{ext}(x,y) are constant in the subdomains. The source Q_{ext} = 1 in area 1 and zero elsewhere. The boundary conditions for this problem are zero Dirichlet (right and top edges) and zero Neumann (bottom and left edges). Sample results of this computation are shown below.

Solution: