Direct solution of the mathematical adjoint equations for an interface current nodal formulation.

摘要

A numerical method for directly computing the mathematical adjoint flux moments and partial currents for the hexagonal-Z geometry interface current nodal formulation in the DIF3D code is described. The new scheme is developed as an alternative to an existing scheme that employs a similarity transformation of the physical adjoint solution to compute the mathematical adjoint. Whereas the existing scheme is rigorous only when the flat transverse-leakage approximation is employed, this new scheme is exact for all leakage approximations in the DIF3D nodal method. in the new scheme, adjoint nodal equations whose form is very similar to that of the forward nodal equations are derived by employing linear combinations of the adjoint partial currents as computational unknowns in the adjoint equations. This enables the use of the forward solution algorithm with only minor modifications for solving the mathematical adjoint equations. By using the new scheme as a reference method, it is shown numerically that while the results computed with the existing scheme are approximate, they are sufficiently accurate for calculations of global and local reactivity changes resulting from coolant voiding in a liquid metal reactor.