Pseudo-compressibility, Dispersive Model and Acoustic Waves in Shallow Water Flows

Anne Sophie Bonnet-Ben Dhia; Marie Odile Bristeau; Edwige Godlewski; Sébastien Impériale; Anne Mangeney; Jacques Sainte-Marie

doi:10.1007/978-3-030-72850-2_10

Pseudo-compressibility, Dispersive Model and Acoustic Waves in Shallow Water Flows

Anne Sophie Bonnet-Ben Dhia
, Marie Odile Bristeau
, Edwige Godlewski
, Sébastien Impériale
, Anne Mangeney
, Jacques Sainte-Marie

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

In this paper we study a dispersive shallow water type model derived from the free surface compressible Navier-Stokes system. The compressible effects allow to capture the acoustic-like waves propagation and can be seen as a relaxation of an underlying incompressible model. The first interest of such a model is thus to capture both acoustic and water waves. The second interest lies in its numerical approximation. Indeed, at the discrete level, the pseudo-compressibility terms circumvent the resolution of an elliptic equation to capture the non-hydrostatic part of the pressure. This drastically reduces the cost of the numerical resolution of dispersive models especially in 2d and 3d.

Original language	English
Title of host publication	SEMA SIMAI Springer Series
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	209-250
Number of pages	42
DOIs	https://doi.org/10.1007/978-3-030-72850-2_10
Publication status	Published - 1 Jan 2021
Externally published	Yes

Publication series

Name	SEMA SIMAI Springer Series
Volume	28
ISSN (Print)	2199-3041
ISSN (Electronic)	2199-305X

Keywords

Compressible models
Dispersive models
Finite volumes
Projection-correction schemes
Shallow water flows
Water and acoustic waves

Access to Document

10.1007/978-3-030-72850-2_10

Cite this

Bonnet-Ben Dhia, A. S., Bristeau, M. O., Godlewski, E., Impériale, S., Mangeney, A., & Sainte-Marie, J. (2021). Pseudo-compressibility, Dispersive Model and Acoustic Waves in Shallow Water Flows. In SEMA SIMAI Springer Series (pp. 209-250). (SEMA SIMAI Springer Series; Vol. 28). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-72850-2_10

@inbook{0d5cd14f81484d7d9caf83c18c59c9d7,

title = "Pseudo-compressibility, Dispersive Model and Acoustic Waves in Shallow Water Flows",

abstract = "In this paper we study a dispersive shallow water type model derived from the free surface compressible Navier-Stokes system. The compressible effects allow to capture the acoustic-like waves propagation and can be seen as a relaxation of an underlying incompressible model. The first interest of such a model is thus to capture both acoustic and water waves. The second interest lies in its numerical approximation. Indeed, at the discrete level, the pseudo-compressibility terms circumvent the resolution of an elliptic equation to capture the non-hydrostatic part of the pressure. This drastically reduces the cost of the numerical resolution of dispersive models especially in 2d and 3d.",

keywords = "Compressible models, Dispersive models, Finite volumes, Projection-correction schemes, Shallow water flows, Water and acoustic waves",

author = "\{Bonnet-Ben Dhia\}, \{Anne Sophie\} and Bristeau, \{Marie Odile\} and Edwige Godlewski and S{\'e}bastien Imp{\'e}riale and Anne Mangeney and Jacques Sainte-Marie",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.",

year = "2021",

month = jan,

day = "1",

doi = "10.1007/978-3-030-72850-2\_10",

language = "English",

series = "SEMA SIMAI Springer Series",

publisher = "Springer Science and Business Media Deutschland GmbH",

pages = "209--250",

booktitle = "SEMA SIMAI Springer Series",

}

Pseudo-compressibility, Dispersive Model and Acoustic Waves in Shallow Water Flows. / Bonnet-Ben Dhia, Anne Sophie; Bristeau, Marie Odile; Godlewski, Edwige et al.
SEMA SIMAI Springer Series. Springer Science and Business Media Deutschland GmbH, 2021. p. 209-250 (SEMA SIMAI Springer Series; Vol. 28).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

TY - CHAP

T1 - Pseudo-compressibility, Dispersive Model and Acoustic Waves in Shallow Water Flows

AU - Bonnet-Ben Dhia, Anne Sophie

AU - Bristeau, Marie Odile

AU - Godlewski, Edwige

AU - Impériale, Sébastien

AU - Mangeney, Anne

AU - Sainte-Marie, Jacques

PY - 2021/1/1

Y1 - 2021/1/1

N2 - In this paper we study a dispersive shallow water type model derived from the free surface compressible Navier-Stokes system. The compressible effects allow to capture the acoustic-like waves propagation and can be seen as a relaxation of an underlying incompressible model. The first interest of such a model is thus to capture both acoustic and water waves. The second interest lies in its numerical approximation. Indeed, at the discrete level, the pseudo-compressibility terms circumvent the resolution of an elliptic equation to capture the non-hydrostatic part of the pressure. This drastically reduces the cost of the numerical resolution of dispersive models especially in 2d and 3d.

AB - In this paper we study a dispersive shallow water type model derived from the free surface compressible Navier-Stokes system. The compressible effects allow to capture the acoustic-like waves propagation and can be seen as a relaxation of an underlying incompressible model. The first interest of such a model is thus to capture both acoustic and water waves. The second interest lies in its numerical approximation. Indeed, at the discrete level, the pseudo-compressibility terms circumvent the resolution of an elliptic equation to capture the non-hydrostatic part of the pressure. This drastically reduces the cost of the numerical resolution of dispersive models especially in 2d and 3d.

KW - Compressible models

KW - Dispersive models

KW - Finite volumes

KW - Projection-correction schemes

KW - Shallow water flows

KW - Water and acoustic waves

UR - https://www.scopus.com/pages/publications/85107075230

U2 - 10.1007/978-3-030-72850-2_10

DO - 10.1007/978-3-030-72850-2_10

M3 - Chapter

AN - SCOPUS:85107075230

T3 - SEMA SIMAI Springer Series

SP - 209

EP - 250

BT - SEMA SIMAI Springer Series

PB - Springer Science and Business Media Deutschland GmbH

ER -

Pseudo-compressibility, Dispersive Model and Acoustic Waves in Shallow Water Flows

Abstract

Publication series

Keywords

Access to Document

Other files and links

Fingerprint

Cite this