A covariance model for Markov statistics

We propose a model to compute the variances for the ensemble average material fluxes in line Markov statistics. The model is exact at the limit of collisionless transport. The calculation of the material flux variances needs the determination of the covariances (in μ and μ′) and we have developed a system of coupled equations and made the usual heuristic extension to the case with collisions. A simple numerical solution, based on the standard discrete ordinates approximation with the diamond discretization, is proposed in 1D slabs. Numerical applications are given for bimaterial homogeneous statistics. The results are encouraging but further research is needed in this area. This will involve a modification of the standard Levermore-Pomraning model.