Some improvements in variational flux synthesis methods

Abstract

In this work a variational synthesis model is proposed for combined space-time flux synthesis with discontinuities allowed in both space and time. Modifications are proposed which eliminate the anomalies noted in existing models at spatial and temporal interfaces of discontinuity. Three types of functional are proposed based on a consistent application of the semi-direct method of the calculus of variations. No difficulties exist for integrations across the points of discontinuity. The equivalence of these three forms for a given choice of the trial-weight function expansions is demonstrated. The Euler-Lagrange equations obtained are in analytic form and are the same for each case. The resulting synthesis model includes the proper asymmetric weighting of the temporal interfaces for initial-final value problems and provides two choices of mixed weighting of the spatial interface conditions. The model also provides variationally imposed boundary and initial-final value conditions and includes delayed neutron contributions. While the analytic system of equations (Euler-Lagrange equations) in the undetermined mixing functions can be solved numerically in the most appropriate and efficient manner, a simple finite difference representation is chosen here for test purposes. Numerical results are reported for a 2 group, 2D, time dependent problem and a comparison made with the TWIGL code. Although the capabilities of the test code are rather limited, these preliminary results are indicative of the potential of the full model. Some observations on the choice of spatial interface weighting are also included.