Shock wave propagation of circular dam break problems

Sudi Mungkasi

doi:10.1088/1742-6596/539/1/012022

Abstract

We examine the behavior of shock wave propagation of circular (radial) dam break problems. A dam break problem represents a reservoir having two sides of water at rest initially with different depth separated by a wall, then water flows after the wall is removed. The behavior of shock wave propagation is investigated with respect to water levels and with respect to the speeds of the shock waves. To the author's knowledge, such investigation for circular dam break problems had never been done before. Therefore, this new work shall be important for applied computational mathematics and physics communities as well as fluid dynamic researchers. Based on our research results, the propagation speed of shock wave in a circular dam break is lower than that of shock wave in a planar dam break having the same initial water levels as in the circular dam break.

Highlights

Water can flow in either a closed or open space
The circular dam break problem can be modelled by the the one-dimensional shallow water equations with varying width as well as the standard two-dimensional shallow water equations
We have presented research results on the shock wave propagation of a circular dam break problem

Summary

Introduction

Water can flow in either a closed or open space. An example of water motion in a closed channel is pipe flows. The circular dam break problem can be modelled by the the one-dimensional shallow water equations with varying width as well as the standard two-dimensional shallow water equations. A simulation of the problem through the one-dimensional shallow water equations with varying width was conducted by Roberts and Wilson [5]. We implement the one-dimensional shallow water equations with varying width following Roberts and Wilson [5]. 3. Numerical method The finite volume method of Roberts and Wilson [5] is used to solve the shallow water equations (1) and (2). For more details on this finite volume method for solving the shallow water equations (1) and (2), we refer to Roberts and Wilson [5]. 4. Numerical results To achieve the goal of this paper we consider a circular dam break problem. All quantities are given in SI units, so we omit the writing of units as they are already clear

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Conclusions