Transport Synthetic Acceleration for Long-Characteristics Assembly-Level Transport Problems Academic Article uri icon

abstract

  • We apply the transport synthetic acceleration (TSA) scheme to the long-characteristics spatial discretization for the two-dimensional assembly-level transport problem. This synthetic method employs a simplified transport operator as its low-order approximation. Thus, in the acceleration step, we take advantage of features of the long-characteristics discretization that make it particularly well suited to assembly-level transport problems. Our main contribution is to address difficulties unique to the long-characteristics discretization and produce a computationally efficient acceleration scheme. The combination of the long-characteristics discretization, opposing reflecting boundary conditions (which are present in assembly-level transport problems), and TSA presents several challenges. We devise methods for overcoming each of them in a computationally efficient way. Since the boundary angular data exist on different grids in the high- and low-order problems, we define restriction and prolongation operations specific to the method of long characteristics to map between the two grids. We implement the conjugate gradient (CG) method in the presence of opposing reflection boundary conditions to solve the TSA low-order equations. The CG iteration may be applied only to symmetric positive definite (SPD) matrices; we prove that the long-characteristics discretization yields an SPD matrix. We present results of our acceleration scheme on a simple test problem, a typical pressurized water reactor assembly, and a typical boiling water reactor assembly.

author list (cited authors)

  • Zika, M. R., & Adams, M. L.

citation count

  • 14

publication date

  • February 2000