Mathematical Modelling of One-dimensional Fluid Flows Bounded by a Free Surface and an Impenetrable Bottom

S. Deryabin, A. Mezentsev

2022

Abstract

The paper investigates a one-dimensional model of a wave coming ashore with a subsequent collapse. For modelling, a system of shallow water equations is taken, which considers the effect of gravity. A non-stationary self-similar variable is introduced in the system of shallow water equations. For a system of equations written in new variables, a boundary condition on the sound characteristic is formulated. The power series is used to construct the solution. Algebraic and ordinary differential equations are solved to find the coefficients of the series. The convergence of this series is proved. The locally analytical solution of the problem of wave overturning in the space of physical variables is constructed. The obtained analytical solutions can be useful for setting boundary and initial conditions in numerical simulation of a tsunami wave over a long period of time.

Paper Citation

in Harvard Style

Deryabin S. and Mezentsev A. (2022). Mathematical Modelling of One-dimensional Fluid Flows Bounded by a Free Surface and an Impenetrable Bottom. In Proceedings of the 1st International Scientific and Practical Conference on Transport: Logistics, Construction, Maintenance, Management - Volume 1: TLC2M; ISBN 978-989-758-606-4, SciTePress, pages 266-271. DOI: 10.5220/0011582800003527

in Bibtex Style

@conference{tlc2m22,
author={S. Deryabin and A. Mezentsev},
title={Mathematical Modelling of One-dimensional Fluid Flows Bounded by a Free Surface and an Impenetrable Bottom},
booktitle={Proceedings of the 1st International Scientific and Practical Conference on Transport: Logistics, Construction, Maintenance, Management - Volume 1: TLC2M},
year={2022},
pages={266-271},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0011582800003527},
isbn={978-989-758-606-4},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 1st International Scientific and Practical Conference on Transport: Logistics, Construction, Maintenance, Management - Volume 1: TLC2M
TI - Mathematical Modelling of One-dimensional Fluid Flows Bounded by a Free Surface and an Impenetrable Bottom
SN - 978-989-758-606-4
AU - Deryabin S.
AU - Mezentsev A.
PY - 2022
SP - 266
EP - 271
DO - 10.5220/0011582800003527
PB - SciTePress