Laterally Averaged Hydrodynamics Model for Reservoir Predictions

Abstract

This paper describes in detail a new two‐dimensional transient model for the prediction of thermally stratified reservoir flows. Unlike many other reservoir models, the present model does not employ the hydrostatic approximation. The full general orthogonal three‐dimensional anelastic equations of motion are laterally averaged to produce a set of two‐dimensional equations in a vertical plane that is oriented along the principal axis of the reservoir. Using an orthogonal boundary fitted mesh, the governing differential equations are rendered discrete by a finite volume technique. The resulting set of coupled difference equations for momentum, mass, and energy are solved by a method that is especially appropriate to reservoirs in which the depth is small compared to the length. Comparisons between the predictions of the model and the flume data of Johnson are presented. These comparisons show that the model is well able to predict the important features of density underflows.