A momentum conservative finite-volume scheme on a staggered z-layer grid for three-dimensional non-hydrostatic flow

Abstract

In the early 90’ the research institute Deltares began the development of a non-hydrostatic extension for the existing three-dimensional shallow-water simulation software Delft3D-FLOW a modeling package which was originally intended for hydrostatic shallow-water flow. The original non-hydrostatic flow model is based on a non-conservative finite-difference discretization of the momentum equations. A model study demonstrated improved performance of conservative discretization schemes over non-conservative scheme for strongly varying and convection-dominated flow. For non-hydrostatic flow a momentum conservative finite-volume discretization is more appropriate. A three-dimensional finite-volume scheme on staggered z-layer grids is presented with improved momentum conservation properties. For simulations of dynamic flow the conservation properties in time of the numerical scheme become more important. Since many typical non-hydrostatic flow situations do not concern steady state calculations, also attention is paid to the momentum conservation properties of the model in time. For strongly non-hydrostatic flow simulations the treatment of the bottom and free-surface becomes of large importance. The design of the finite-volume discretization gave the opportunity to have a renewed look on of the existing Delft3D z-layer model. Simulations have been carried out of short waves in a basin. The results showed an improvement compared with the existing finite-difference method and brought to the attention other aspects of the existing discretization that demand improvement in order to make the model suitable for strongly non-hydrostatic, convection-dominated flow.