Tag Archives: sigma-mesh

Accurate vertical profiles of turbulent flow in z-layer models

F.W. Platzek, G.S. Stelling, J.A. Jankowski and J.D. Pietrzak

Abstract. Three-dimensional hydrodynamic z-layer models, which are used for simulating the flow in rivers, estuaries, and oceans, suffer from an inaccurate and often discontinuous bottom shear stress representation, due to the staircase bottom. We analyze the governing equations and clearly show the cause of the inaccuracies. Based on the analysis, we present a new method that significantly reduces the errors and the grid dependency of the results. Continue reading

On the representation of bottom shear stress in z-layer models

F. Platzek, G.S. Stelling, J.A. Jankowski, R. Patzwahl

Abstract. Bottom friction plays an important role in modelling river flows. In three-dimensional (3D) models, the vertical discretization is commonly based on σ-layers or z-layers. In this paper we focus on a well-known problem encountered when applying z-layers: local truncation errors in the computation of bottom shear stress and near-bed turbulence along a sloping bottom as e.g. in the case of 3D river simulations. This problem stems from the ‘staircase’ representation of the bottom and results in difficulties in the computation of morphological changes. Continue reading

A non-hydrostatic model for free surface flows

Jacek A. Jankowski

PhD thesis Abstract

An algorithm for solution of three-dimensional Navier-Stokes equations for incompressible free surface flows is developed. A decoupled algorithm based on the fractional step (operator-splitting) technique is applied. The solution is obtained in subsequent stages treating equations split into parts having well-defined mathematical properties, so that the most adequate methods for a given differential operator type can be used. The decoupled algorithm structure, which does not use the continuity equation explicitly, allows application of equal-order linear interpolation functions for all variables. The applied reference element type, a prism with six nodes and linear interpolation functions, is a compromise between the exactness of the interpolation, model complexity and computational cost. The finite difference method is applied for the time discretisation and the computational domain variability is taken into account by a standard sigma-mesh structure which is well suited to most geophysical applications. Continue reading

Ein nicht-hydrostatisches Modell für Strömungen mit freier Oberfläche

Ein nicht-hydrostatisches Modell für Strömungen mit freier Oberfläche, Promotionsvortrag, 12. November 1998, Institut für Strömungsmechanik und Elektronisches Rechnen im Bauwesen der Universität Hannover. Continue reading