A Godunov-type scheme and a relaxation scheme for second-order turbulence-moment models

Nadjib Bennoura Bouchiba; Martin Ferrand; Jean Marc Hérard

doi:10.1051/m2an/2025066

A Godunov-type scheme and a relaxation scheme for second-order turbulence-moment models

Nadjib Bennoura Bouchiba, Martin Ferrand, Jean Marc Hérard

Lamsid/EDF/R and D

Research output: Contribution to journal › Article › peer-review

Abstract

A Godunov-type scheme and a relaxation scheme are presented to approximate the solutions of the convective subsystem arising from the transport equations of a class of second-order turbulence-moment models in the framework of incompressible flows. An analytical representation is proposed for the case of the occurrence of a non-turbulent region. Numerical tests of the two schemes and a comparison with a Rusanov scheme complete the paper.

Original language	English
Pages (from-to)	2639-2683
Number of pages	45
Journal	Mathematical Modelling and Numerical Analysis
Volume	59
Issue number	5
DOIs	https://doi.org/10.1051/m2an/2025066
Publication status	Published - 1 Sept 2025
Externally published	Yes

Keywords

Godunov scheme
Riemann problem
Second-order turbulence-moment models
incompressible flows
laminar/turbulent flows
relaxation scheme

Access to Document

10.1051/m2an/2025066

Cite this

@article{2a01a6e17e3540b1bbd154a311e905e9,

title = "A Godunov-type scheme and a relaxation scheme for second-order turbulence-moment models",

abstract = "A Godunov-type scheme and a relaxation scheme are presented to approximate the solutions of the convective subsystem arising from the transport equations of a class of second-order turbulence-moment models in the framework of incompressible flows. An analytical representation is proposed for the case of the occurrence of a non-turbulent region. Numerical tests of the two schemes and a comparison with a Rusanov scheme complete the paper.",

keywords = "Godunov scheme, Riemann problem, Second-order turbulence-moment models, incompressible flows, laminar/turbulent flows, relaxation scheme",

author = "Bouchiba, \{Nadjib Bennoura\} and Martin Ferrand and H{\'e}rard, \{Jean Marc\}",

note = "Publisher Copyright: {\textcopyright} The authors. Published by EDP Sciences, SMAI 2025.",

year = "2025",

month = sep,

day = "1",

doi = "10.1051/m2an/2025066",

language = "English",

volume = "59",

pages = "2639--2683",

journal = "Mathematical Modelling and Numerical Analysis",

issn = "0764-583X",

number = "5",

}

TY - JOUR

T1 - A Godunov-type scheme and a relaxation scheme for second-order turbulence-moment models

AU - Bouchiba, Nadjib Bennoura

AU - Ferrand, Martin

AU - Hérard, Jean Marc

N1 - Publisher Copyright: © The authors. Published by EDP Sciences, SMAI 2025.

PY - 2025/9/1

Y1 - 2025/9/1

N2 - A Godunov-type scheme and a relaxation scheme are presented to approximate the solutions of the convective subsystem arising from the transport equations of a class of second-order turbulence-moment models in the framework of incompressible flows. An analytical representation is proposed for the case of the occurrence of a non-turbulent region. Numerical tests of the two schemes and a comparison with a Rusanov scheme complete the paper.

AB - A Godunov-type scheme and a relaxation scheme are presented to approximate the solutions of the convective subsystem arising from the transport equations of a class of second-order turbulence-moment models in the framework of incompressible flows. An analytical representation is proposed for the case of the occurrence of a non-turbulent region. Numerical tests of the two schemes and a comparison with a Rusanov scheme complete the paper.

KW - Godunov scheme

KW - Riemann problem

KW - Second-order turbulence-moment models

KW - incompressible flows

KW - laminar/turbulent flows

KW - relaxation scheme

UR - https://www.scopus.com/pages/publications/105016907979

U2 - 10.1051/m2an/2025066

DO - 10.1051/m2an/2025066

M3 - Article

AN - SCOPUS:105016907979

SN - 0764-583X

VL - 59

SP - 2639

EP - 2683

JO - Mathematical Modelling and Numerical Analysis

JF - Mathematical Modelling and Numerical Analysis

IS - 5

ER -

A Godunov-type scheme and a relaxation scheme for second-order turbulence-moment models

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this