9. Deterministic Transport

Introduction by S. M. Bowman

SCALE deterministic transport capabilities enable criticality safety, depletion, sensitivity, and uncertainty analysis, as well as hybrid approaches to Monte Carlo analysis. SCALE provides a one-dimensional (1D) transport solver for eigenvalue neutronics and fixed source neutron-gamma analysis with XSDRN, two-dimensional (2D) eigenvalue neutronics with NEWT, and a three-dimensional (3D) transport solver for hybrid acceleration of Monte Carlo fixed source and eigenvalue calculations with Denovo. Generally, the use of these transport solvers in SCALE is best accessed through the capability specific sequences: CSAS for criticality safety, TRITON for 1D and 2D depletion, TSUNAMI-1D for sensitivity and uncertainty analysis, and MAVRIC for 3D fixed source hybrid Monte Carlo analysis.


XSDRN is a multigroup discrete-ordinates code that solves the 1D Boltzmann equation in slab, cylindrical, or spherical coordinates. Alternatively, the user can select P1 diffusion theory, infinite medium theory, or Bn theory. A variety of calculational types is available, including fixed source, eigenvalue, or search calculations. In SCALE, XSDRN is used for several purposes: eigenvalue (keff) determination; cross section collapsing; and computation of fundamental-mode or generalized adjoint functions for sensitivity analysis.


NEWT (New ESC-based Weighting Transport code) is a multigroup discrete-ordinates radiation transport computer code with flexible meshing capabilities that allow 2D neutron transport calculations using complex geometric models. The differencing scheme employed by NEWT-the Extended Step Characteristic approach-allows a computational mesh based on arbitrary polygons. Such a mesh can be used to closely approximate curved or irregular surfaces to provide the capability to model problems that were formerly difficult or impractical to model directly with discrete-ordinates methods. Automated grid generation capabilities provide a simplified user input specification in which elementary bodies can be defined and placed within a problem domain. NEWT can be used for eigenvalue, critical-buckling correction, and source calculations, and it can be used to prepare collapsed weighted cross sections in AMPX working library format.

Like other SCALE modules, NEWT can be run as a standalone module or as part of a SCALE sequence. NEWT has been incorporated into SCALE TRITON control module sequences. TRITON can be used simply to prepare cross sections for a NEWT transport calculation and then automatically execute NEWT. TRITON also provides the capability to perform 2D depletion calculations in which the transport capabilities of NEWT are combined with multiple ORIGEN depletion calculations to perform 2D depletion of complex geometries. In the TRITON depletion sequence, NEWT can also be used to generate lattice-physics parameters and cross sections for use in subsequent nodal core simulator calculations.


Denovo [DTESSC10], is a parallel 3D discrete-ordinates code available in SCALE as part of two control module sequences for different applications, as described below. Because Denovo can only be run in SCALE via the Monaco with Automated Variance Reduction using Importance Calculations (MAVRIC) or Denovo Eigenvalue Calculation (DEVC), it is not documented separately in the section entitled “Deterministic Transport” in this manual.

The MAVRIC hybrid Monte Carlo radiation shielding sequence employs the Consistent Adjoint Driven Importance Sampling (CADIS) and Forward-Weighted CADIS (FW-CADIS) methodologies. Denovo is used to generate adjoint (and, for FW-CADIS, forward) scalar fluxes for the CADIS methods in MAVRIC. This adjoint flux information is then used by MAVRIC to construct a space- and energy-dependent importance map (i.e., weight windows) to be used for biasing during Monte Carlo particle transport and as a mesh-based biased source distribution. For use in MAVRIC/CADIS, it is highly desirable that the SN code be fast, positive, and robust. The phase-space shape of the forward and adjoint fluxes, as opposed to a highly accurate solution, is the most important quality for Monte Carlo weight-window generation. Accordingly, Denovo provides a step-characteristics spatial differencing option that produces positive scalar fluxes as long as the source (volume plus in-scatter) is positive. Denovo uses an orthogonal, nonuniform mesh that is ideal for CADIS applications because of the speed and robustness of calculations on this mesh type. Denovo can be run stand-alone in MAVRIC to perform fixed source calculations using the PARM=forward (for forward Denovo) or PARM=adjoint (for adjoint Denovo). See the MAVRIC chapter for details.

The other sequence that uses Denovo is the DEVC sequence. DEVC generates a reasonably accurate starting source through a Denovo eigenvalue calculation. Denovo can be run stand-alone in DEVC for calculating criticality eigenvalue problems. This sequence reads an input file very similar to a CSAS6 input file that contains an extra block of input for describing the Denovo mesh grid and calculational parameters.



Thomas M. Evans, Alissa S. Stafford, Rachel N. Slaybaugh, and Kevin T. Clarno. Denovo: A new three-dimensional parallel discrete ordinates code in SCALE. Nuclear technology, 171(2):171–200, 2010.