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:
nce the actual motion and temperature always have stochastic components, deterministic methods must relate these components to time-averaged quantities in order that closure of the governing equations can be achieved. This having been done, the solutions to the basic hydrothermal equations may be determined either analytically or numerically. Analytical solution refers to the closed form integration of the governing equations. As disc'ussed earlier, this method is possible only for highly simplified cases. It is seldom possible to obtain analytical solutions for time-dependent flow fields or complex receiving water geometry. Consequently, the utility of any analytical solution should be very carefully assessed by the modeler to ascertain the conditions under which the model might be a valid predictive tool. From a practical point of view, the attractiveness and elegance of analytical solutions are often vitiated by the fact that the models from which they stem have been simplified to the point that they no longer adequately simulate the prototype. Hence, in predictive far-field modeling of complex systems, physically realistic solutions might require the rather early abandonment of analytical solutions in favor of numerical methods. The most widely used numerical solution technique for far-field model equations is the method of finite differences. The fundamental principle of this method is the subdivision of the solution region into a number of discrete grid points at which the derivatives in the governing equations are approximated by finite differences. There are several approximation schemes in current use, the most popular of which are truncated Taylor's series and the treatment of individual grid meshes as discrete control volumes. Sophisticated forms of finite difference 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