Heterogeneous variational nodal method

Traditional nodal methods all belong to homogeneous nodal method which requires homogeneous cross section in each node. The error introduced by the approximation of homogeneity can be accepted in solid nuclear fuel reactors. However, in molten salt reactor (MSR), the fluid fuel has continuous changing cross sections caused by the continuous temperature and nuclide density distributions which makes it difficult for traditional nodal method to obtain both high accuracy and efficiency. To solve this problem, the variational nodal method was generalized for heterogeneous node with diffusion approximation to handle continuous cross section in one dimensional slab geometry, and the code Violet-Het1D was developed. Numerical results show that with the same number of node and expansion order, the heterogeneous variational nodal method obtains higher accuracy than homogeneous variational nodal method without decreasing the efficiency.