Nonhydrostatic Three-Dimensional Model for Hydraulic Flow Simulation. I: Formulation and Verification

A three-dimensional numerical method, without the hydrostatic assumption, is developed to solve flow problems in hydraulic engineering. This method adopts an unstructured grid technology that is applicable to arbitrarily shaped cells and offers the potential to unify many grid topologies into a single formulation. It solves the three-dimensional turbulent flow equations and utilizes a collocated and cell-centered storage scheme with a finite-volume discretization. In Part I, the technical details of the method are presented, along with its verification and validation by computing a benchmark open channel flow. Meshes of hexahedral, tetrahedral, and prismatic shapes are employed, and results are compared with experimental data and among different meshes. Accuracy estimates and error analyses are also developed and discussed. Our companion paper applies the method to two practical problems: Flow in a hydroturbine draft tube, and flow in the forebay of Rocky Reach Dam for design of a fish passage facility.