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(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).

Sample results


Solution to the iron-water example.

Final mesh (h-FEM with linear elements):

Final finite element mesh for the iron-water example (h-FEM with linear elements).

Final mesh (h-FEM with quadratic elements):

Final finite element mesh for the iron-water example (h-FEM with quadratic elements).

Final mesh (hp-FEM):

Final finite element mesh for the iron-water example (hp-FEM).

DOF convergence graphs:

DOF convergence graph for example iron-water.

CPU time convergence graphs:

CPU convergence graph for example iron-water.

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