Iron-Water¶

Loading mesh in ExodusII format¶

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:

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

Problem description¶

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

(1) $-\nabla \cdot (D(x,y) \nabla \Phi) + \Sigma_a(x,y) \Phi - Q_{ext}(x,y) = 0.$

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).