Efficient parallel solution of the 3D stationary Boltzmann transport equation for diffusive problems

Abstract

This paper presents an efficient parallel method for the deterministic solution of the 3D stationary Boltzmann transport equation applied to diffusive problems such as nuclear core criticality computations. Based on standard MultiGroup-Sn-DD discretization schemes, our approach combines a highly efficient nested parallelization strategy [1] with the PDSA parallel acceleration technique [2] applied for the first time to 3D transport problems. These two key ingredients enable us to solve extremely large neutronic problems involving up to 10 12 degrees of freedom in less than an hour using 64 super-computer nodes.

Piecewise Diffusion Synthetic Acceleration scheme for neutron transport simulations in optically thick systems

“…Subtracting (10) to (11), rearranging the terms, and restricting it to D 1 , we find that δ |D1 verifies…”

“…The implementation of PDSA only requires having a standard neutron diffusion solver whose discretization is consistent with that of the neutron transport solver. In practice, and as explained in [11], starting from an initially sequential DSA-accelerated transport code, one only needs to take care of the parallelization of the transport solver; the parallel acceleration scheme comes at no practical development cost.…”

“…The implementation of PDSA only requires having a standard neutron diffusion solver whose discretization is consistent with that of the neutron transport solver. In practice, and as explained in [11], starting from an…”

“…We study here the PDSA scheme as a perturbation of the DSA scheme. We therefore consider the error introduced by the Neumann Diffusion problem (11), with respect to the global diffusion problem (10):…”

“…We will focus here on the definition of the PDSA scheme, and on the proof that it converges at the continuous level, along with simple 1D numerical experiments. We show in a companion paper [11] how this has been implemented in EDF's COCAGNE [12] platform, which features a diamond-difference S N transport solver, accelerated by an SP 1 solver using mixed dual Raviart-Thomas (RT k ) finite elements [13,6].…”