A conservative scheme for simulation of free-surface turbulent and wave flows

Anqing Xuan, Lian Shen

Research output: Contribution to journalArticle

Abstract

A numerical scheme with good conservation properties is developed for the simulation of free-surface turbulent and viscous wave flows using a surface-fitted curvilinear grid. The Navier–Stokes equations are written in a strong conservative formulation with respect to the curvilinear coordinates, and are discretized by a pseudo-spectral method in the horizontal directions and a finite-difference method in the vertical direction. Large-eddy simulation (LES) is implemented with the conservative scheme to extend the simulation capability to turbulent flows with higher Reynolds numbers. Fully nonlinear kinematic and dynamic boundary conditions are implemented at the free surface. The numerical scheme is validated using a variety of wave and vortical flow test cases. The results show good agreement with previous theoretical and numerical predictions, whereas the present scheme achieves significant improvement in the conservation of mass and momentum over the non-conservative scheme developed by Yang & Shen [1]. Meanwhile, the present conservative scheme is found to be more stable than the non-conservative scheme for the simulation of sideband waves and broadband waves. The effect of viscous dissipation on the long-term nonlinear wave evolution is also captured by the present scheme. The ability of the present scheme for simulating long-term wave-current-turbulence interaction is demonstrated by the computation of Langmuir circulation, for which the non-conservative scheme produces significant errors in mass and momentum conservation and the simulation fails. Flow features of the Langmuir circulation, such as the counter-rotating vortices and converging-diverging zones, have been successfully captured with our numerical scheme. The turbulence statistics also agree with the characteristics of Langmuir circulation.

Original languageEnglish (US)
Pages (from-to)18-43
Number of pages26
JournalJournal of Computational Physics
Volume378
DOIs
StatePublished - Feb 1 2019

Fingerprint

turbulent flow
conservation
Conservation
simulation
Momentum
Turbulence
turbulence
momentum
spherical coordinates
spectral methods
high Reynolds number
Large eddy simulation
large eddy simulation
sidebands
Finite difference method
Turbulent flow
Kinematics
counters
Vortex flow
Reynolds number

Keywords

  • Conservation
  • Free-surface flow
  • Turbulence
  • Wave

Cite this

A conservative scheme for simulation of free-surface turbulent and wave flows. / Xuan, Anqing; Shen, Lian.

In: Journal of Computational Physics, Vol. 378, 01.02.2019, p. 18-43.

Research output: Contribution to journalArticle

@article{8ff7953bb0654ecca00214e9842cc307,
title = "A conservative scheme for simulation of free-surface turbulent and wave flows",
abstract = "A numerical scheme with good conservation properties is developed for the simulation of free-surface turbulent and viscous wave flows using a surface-fitted curvilinear grid. The Navier–Stokes equations are written in a strong conservative formulation with respect to the curvilinear coordinates, and are discretized by a pseudo-spectral method in the horizontal directions and a finite-difference method in the vertical direction. Large-eddy simulation (LES) is implemented with the conservative scheme to extend the simulation capability to turbulent flows with higher Reynolds numbers. Fully nonlinear kinematic and dynamic boundary conditions are implemented at the free surface. The numerical scheme is validated using a variety of wave and vortical flow test cases. The results show good agreement with previous theoretical and numerical predictions, whereas the present scheme achieves significant improvement in the conservation of mass and momentum over the non-conservative scheme developed by Yang & Shen [1]. Meanwhile, the present conservative scheme is found to be more stable than the non-conservative scheme for the simulation of sideband waves and broadband waves. The effect of viscous dissipation on the long-term nonlinear wave evolution is also captured by the present scheme. The ability of the present scheme for simulating long-term wave-current-turbulence interaction is demonstrated by the computation of Langmuir circulation, for which the non-conservative scheme produces significant errors in mass and momentum conservation and the simulation fails. Flow features of the Langmuir circulation, such as the counter-rotating vortices and converging-diverging zones, have been successfully captured with our numerical scheme. The turbulence statistics also agree with the characteristics of Langmuir circulation.",
keywords = "Conservation, Free-surface flow, Turbulence, Wave",
author = "Anqing Xuan and Lian Shen",
year = "2019",
month = "2",
day = "1",
doi = "10.1016/j.jcp.2018.10.046",
language = "English (US)",
volume = "378",
pages = "18--43",
journal = "Journal of Computational Physics",
issn = "0021-9991",
publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - A conservative scheme for simulation of free-surface turbulent and wave flows

AU - Xuan, Anqing

AU - Shen, Lian

PY - 2019/2/1

Y1 - 2019/2/1

N2 - A numerical scheme with good conservation properties is developed for the simulation of free-surface turbulent and viscous wave flows using a surface-fitted curvilinear grid. The Navier–Stokes equations are written in a strong conservative formulation with respect to the curvilinear coordinates, and are discretized by a pseudo-spectral method in the horizontal directions and a finite-difference method in the vertical direction. Large-eddy simulation (LES) is implemented with the conservative scheme to extend the simulation capability to turbulent flows with higher Reynolds numbers. Fully nonlinear kinematic and dynamic boundary conditions are implemented at the free surface. The numerical scheme is validated using a variety of wave and vortical flow test cases. The results show good agreement with previous theoretical and numerical predictions, whereas the present scheme achieves significant improvement in the conservation of mass and momentum over the non-conservative scheme developed by Yang & Shen [1]. Meanwhile, the present conservative scheme is found to be more stable than the non-conservative scheme for the simulation of sideband waves and broadband waves. The effect of viscous dissipation on the long-term nonlinear wave evolution is also captured by the present scheme. The ability of the present scheme for simulating long-term wave-current-turbulence interaction is demonstrated by the computation of Langmuir circulation, for which the non-conservative scheme produces significant errors in mass and momentum conservation and the simulation fails. Flow features of the Langmuir circulation, such as the counter-rotating vortices and converging-diverging zones, have been successfully captured with our numerical scheme. The turbulence statistics also agree with the characteristics of Langmuir circulation.

AB - A numerical scheme with good conservation properties is developed for the simulation of free-surface turbulent and viscous wave flows using a surface-fitted curvilinear grid. The Navier–Stokes equations are written in a strong conservative formulation with respect to the curvilinear coordinates, and are discretized by a pseudo-spectral method in the horizontal directions and a finite-difference method in the vertical direction. Large-eddy simulation (LES) is implemented with the conservative scheme to extend the simulation capability to turbulent flows with higher Reynolds numbers. Fully nonlinear kinematic and dynamic boundary conditions are implemented at the free surface. The numerical scheme is validated using a variety of wave and vortical flow test cases. The results show good agreement with previous theoretical and numerical predictions, whereas the present scheme achieves significant improvement in the conservation of mass and momentum over the non-conservative scheme developed by Yang & Shen [1]. Meanwhile, the present conservative scheme is found to be more stable than the non-conservative scheme for the simulation of sideband waves and broadband waves. The effect of viscous dissipation on the long-term nonlinear wave evolution is also captured by the present scheme. The ability of the present scheme for simulating long-term wave-current-turbulence interaction is demonstrated by the computation of Langmuir circulation, for which the non-conservative scheme produces significant errors in mass and momentum conservation and the simulation fails. Flow features of the Langmuir circulation, such as the counter-rotating vortices and converging-diverging zones, have been successfully captured with our numerical scheme. The turbulence statistics also agree with the characteristics of Langmuir circulation.

KW - Conservation

KW - Free-surface flow

KW - Turbulence

KW - Wave

UR - http://www.scopus.com/inward/record.url?scp=85057248553&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85057248553&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2018.10.046

DO - 10.1016/j.jcp.2018.10.046

M3 - Article

VL - 378

SP - 18

EP - 43

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -