Tag Archives: Navier-Stokes equations

Comparing numerical simulations of free surface flows using non-hydrostatic Navier-Stokes and Boussinesq equations

Jean-Michel Hervouet and Jacek A. Jankowski

Abstract. The numerical solutions of three-dimensional, non-hydrostatic Navier-Stokes equations are compared to the ones obtained with Boussinesq equations in the case of a solitary wave in a rectangular channel. 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