An enhanced geometry-independent mesh weight window generator for MCNP Page: 4 of 10
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An Enhanced Geometry-Independent Mesh Weight Window
Generator for MCNP
T.M. Evans and J.S. Hendricks
A new, enhanced, weight window generator suite has been developed for MCNPTM. The new
generator correctly estimates importances in either an user-specified, geometry-independent orthogonal
grid or in MCNP geometric cells. The geometry-independent option alleviates the need to subdivide the
MCNP cell geometry for variance reduction purposes. In addition, the new suite corrects several
pathologies in the existing MCNP weight window generator. To verify the correctness of the new
implementation, comparisons are performed with the analytical solution for the cell importance. Using the
new generator, differences between Monte Carlo generated and analytical importances are less than 0.1%.
Also, assumptions implicit in the original MCNP generator are shown to be poor in problems with high
scattering media. The new generator is fully compatible with MCNP's AVATARTM automatic variance
reduction method. The new generator applications, together with AVATAR, gives MCNP an enhanced
suite of variance reduction methods. The flexibility and efficacy of this suite is demonstrated in a neutron
porosity tool well-logging problem.
The efficiency of variance reduction schemes in Monte Carlo codes is highly dependent on user insight
and experience. The process may be simplified by incorporating deterministic adjoint solutions as
importance functions for preferential sampling along specific trarlsport paths. This type of automatic
variance reduction is available in several codes.1' The automatic variance reduction scheme in MCNP,
AVATAR, uses an adjoint deterministic solution from THREEDANTTM5 to generate weight windows on a
geometry-independent grid.' We have enhanced AVATAR by developing a weight window generator that
estimates the importances on an user-defined, geometry-independent grid" utilizing the forward-adjoint
method.' The new generator may be used to iterate the adjoint map from THREEDANT, or it may be
used independently of any deterministic calculation. Also, as opposed to the existing MCNP generator, the
new generator is completely automated allowing for easy batch runs of iterated problems.
In addition to providing the geometry-independent functionality, the new generator also correctly
implements the forward-adjoint algorithm as originally postulated by Booth and Hendricks.9 The present
version of the MCNP cell-based generator contains implicit assumptions that were necessary for memory
management issues. In many cases these assumptions are robust; however, in problems with multiple
particles, high secondary particle yields, and highly scattering media the estimated weight windows will not
be optimal. The new generator fixes these assumptions and provides correct estimations of the importance.
In this paper we will demonstrate the accuracy, efficiency, and functionality of the new generator.
First we will derive the analytical solution for the forward importance in slab geometry. These analytical
solutions will be compared to the old and new generator estimates of the importance. After validating the
correctness of the new generator, we will demonstrate its effectiveness and flexibility in a neutron porosity
tool well-logging problem. These calculations will illustrate the capabilities of the new variance reduction
suite in MCNP.
2 VERIFICATION OF THE FORWARD-ADJOINT METHOD
2.1 CALCULATION OF THE IMPORTANCE FUNCTION
Booth10 has prescribed the analytical importance functions in slab geometry. Consider an 1-D slab
with dimensions 0 _< z < T. The importance function is cast as a set of coupled differential equations
featuring the importance of particles moving in the positive z direction and the negative x direction. We
define these importances as the forward importance, N(z), and the backward importance, L(x).
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Evans, T.M. & Hendricks, J.S. An enhanced geometry-independent mesh weight window generator for MCNP, article, December 31, 1997; New Mexico. (digital.library.unt.edu/ark:/67531/metadc711752/m1/4/: accessed February 18, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.