# Simulation of free surface flows with non-hydrostatic pressure distribution

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## Abstract

In this work, a free surface flow simulator is developed in which Navier–Stokes equations using Marker and Cell (MAC) method in the framework of finite difference methodology have been solved. The free surface is tracked by the volume of fluid (VOF) method. The numerical code without free-surface is validated against the flow past a square cylinder. Three different free surface flows, i.e., dam break flow, two-dimensional cavity filling and undular bore, are studied to demonstrate the efficacy of the developed numerical model to simulate free surface flow. The numerical model used in the present work involves tracking of free surface of a single fluid in a two-fluid system. The parameters which can affect the interface orientation of the fluid is given as boundary condition at the interface. The inherent advantage of such numerical models is its ability to track free surface for high density and viscosity ratio fluids like air–water. The numerical model used in the present work is capable of solving such high density ratio two-fluid systems for which the effects due to surface tension are negligible. Results from all the problems are compared with earlier results available in literature.

## Keywords

Navier–Stokes equations volume of fluid method free surface flow dam break flow undular bore## List of symbols

*F*volume fraction of fluid

*g*acceleration due to gravity

- i, j
cell indices in x and y direction

*L*length scale

*p*pressure

*T*time scale

*u*streamwise component of velocity

*v*vertical component of velocity

*vol*(*F)*volume of fluid inside a cell

## Greek symbol

- \( \Delta t \)
time step

- \( \Delta x,\Delta y \)
grid size in x and y direction

## Non-dimensional numbers

*Fr*Froude number

*Re*Reynolds number

*St*Strouhal number

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