No abstract

Investigations of scaling and equilibration of general matrices have been traditionally aimed at the effects on the stability and accuracy of LU factorizations-the so-called scaling problem. Notably, Skeel (1979) concludes that no systematic scaling procedure can be concocted for general matrices exempt from the danger of disastrous effects. Other researchers suggest that scaling procedures are not beneficial and should be abandoned altogether. Stability and accuracy issues notwithstanding, we show that this unglamorous technique has a profound impact on the sparsity of the resulting LU factors. In the modern era of fast computing, equilibration can play a key role in constructing incomplete sparse factorizations to solve a problem unstably, but quickly and iteratively. This article presents practical evidence, on the basis of sparsity, that scaling is an indispensable companion for sparse factorization algorithms when applied to realistic problems of industrial interest. In light of our findings, we conclude that equilibration with the ∞-norm is superior than equilibration with the 2-norm.

No abstract

Plant-level modeling and simulation of a used nuclear fuel prototype dissolver is presented. Emphasis is given in developing a modeling and simulation approach to be explored by other processes involved in the recycle of used fuel. The commonality concepts presented in a previous communication were used to create a model and realize its software module. An initial model was established based on a theory of chemical thermomechanical network transport outlined previously. A software module prototype was developed with the required external behavior and internal mathematical structure.Results obtained demonstrate the generality of the design approach and establish an extensible mathematical model with its corresponding software module for a wide range of dissolvers. Scale up numerical tests were made varying the type of used fuel (breeder and light-water reactors) and the capacity of dissolution (0.5 t d −1 to 1.7 t d −1 ). These tests were motivated by user requirements in the area of nuclear materials safeguards. A computer module written in high-level programing languages (MATLAB and Octave) was developed, tested, and provided as open-source code (MATLAB) for integration into the Separations and Safeguards Performance Model application in development at Sandia National Laboratories.The modeling approach presented here is intended to serve as a template for a rational modeling of all plant-level modules. This will facilitate the practical application of the commonality features underlying the unifying network transport theory proposed recently. In addition, by example, this model describes, explicitly, the needed data from sub-scale models, and logical extensions for future model development. For example, from thermodynamics, an off-line simulation of molecular dynamics could quantify partial molar volumes for the species in the liquid phase; this simulation is currently at reach for high-performance computing. From fluid mechanics, a holdup capacity function is needed for the dissolver device; this simulation is currently at reach for computational fluid mechanics given the existing CAD geometry. From chemical transport phenomena, a simulation of the particle-scale dissolution front is needed to derive an improved solid dissolution kinetics law by predicting the local surface area change; an example was provided in this report. In addition, the associated reaction mechanisms for dissolution are presently largely untested and simplified, hence even a parallel experimental program in reaction kinetics is needed to support modeling and simulation efforts. Last but not least, a simple account of finite rates of solid feed and transfer can be readily introduced via a coupled delayed model.