Document: NRC Regulatory Guide
Document ID: f4c5fb1d-efb9-4168-9804-5ad3f6f64d06
Document Type: regulatory_guide
Title: Reporting Procedure for Mathematical Models Selected To Predict Heated Effluent Dispersion in Natural Water Bodies
Source: NRC Regulatory Guide Division 4
Source URL: https://www.nrc.gov/docs/ML0037/ML003739535.pdf
Revision Date: 2023-06
Chapter: 
Section ID: RG-4.4
CFR Part: 
CFR Title: 

Content:
fference techniques permit variable time steps and grid mesh sizes. This refinement provides considerable computational efficiency and added flexibility in the solution of time-dependent problems with irregular shoreline geometry. In recent years, a somewhat different technique known as the method of finite elements has emerged as a powerful tool for the numerical solution of hydrodynamic transport equations. In this method, the domain of interest is subdivided into a number of "finite elements" interconnected at a discrete number of nodal points. Within each element the dependent variables are approximated by known shape functions whose magnitudes are determined by assumed nodal values. In early applications of the finite element method, solutions were obtained from a discrete set of linear algebraic equations derived through minimization of a functional for the governing differential equation. The application of this method to hydrothermal problems was limited because it was not always possible to find the proper functional. Recently, however, this restriction has been removed through use of Galerkin's method,S in which the set of algebraic equations is obtained directly from the governing differential equation. The approximate solution is obtained not by a variational principle, but rather by orthogonalization of" the solution error with respect to the known shape functions. The finite elements, usually triangular in shape, may be arbitrary in size and arrangement. This flexibility provides a -twofold advantage in that computational resolution can be varied at will throughout the region of interest, and almost any boundary shape can be approximated by the proper choice of triangular elements. (2) Stochatic Models In stochastic dispersion models, the probabilistic behavior of the flow field is handled directly. The most promising stochastic solution technique is the Monte Cado 'method, in which the probabilistic behavior of the 514,._.A. Lotiuk, J. C. Andenon, and