Some analytical solutions for validation of free surface flow computational codes

Bristeau, Marie-Odile; Martino, Bernard Di; Mangeney, A.; Sainte-Marie, Jacques; Souillé, Fabien

doi:10.1017/jfm.2020.1179

Cited by 5 publications

(2 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Additionally, Matskevich and Chubarov (2019) extended the results of Ball and Thacker to include the effects of Coriolis forces and bottom friction. Bristeau et al (2021) also extended the results of Thacker and introduced two respective solutions describing velocity distributed along the vertical axis and velocity accounting for variable density.…”

Section: Introductionmentioning

confidence: 82%

Semi-Analytical Solutions of Shallow Water Waves with Idealised Bottom Topographies

Liu¹,

Clark²

2023

Preprint

View full text Add to dashboard Cite

Analysing two-dimensional shallow water equations with idealised bottom topographies have many applications in the atmospheric and oceanic sciences; however, restrictive flow pattern assumptions have been made to achieve explicit solutions. This work employs the Adomian decomposition method (ADM) to develop semi-analytical formulations of these problems that preserve the direct correlation of the physical parameters while capturing the nonlinear phenomenon. Furthermore, we exploit these techniques as reverse engineering mechanisms to develop key connections between some prevalent ansatz formulations in the open literature as well as derive new families of exact solutions describing geostrophic inertial oscillations and anticyclonic vortices with finite escape times. Our semi-analytical evaluations show the promise of this approach in terms of providing robust approximations against several oceanic variations and bottom topographies while also preserving the direct correlation between the physical parameters such as the Froude number, the bottom topography, the Coriolis parameter, as well as the flow and free surface behaviours. Our numerical validations provide additional confirmations of this approach while also illustrating that ADM can also be used to provide insight and deduce novel solutions that have not been explored, which can be used to characterize various types of geophysical flows.

show abstract

Section: Introductionmentioning

confidence: 82%

Semi-Analytical Solutions of Shallow Water Waves with Idealised Bottom Topographies

Liu¹,

Clark²

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…This is evident in general relativity where gravitational forces are described as curvature of space. Above solitary solutions permit to validate numerical solvers without having to depict complex domain shapes such as parabolic bowls [10]. Also, due to the simplicity of the boundary conditions, these can be imposed on the boundaries of arbitrary domain shapes as long as the domain is permitted to adapt along one dimension to h B .…”

Section: Supplemental Documentmentioning

confidence: 99%

Solitary solution method for incompressible Navier-Stokes PDE

Lawen

2021

Preprint

View full text Add to dashboard Cite

The method exploits the contraction of space to systematically obtain compact solitary solutions. The latter are provided for the incompressible Euler and Navier-Stokes PDE. The nonlinear response of momentum advection is moved into a term for contracting space. Then the linear continuity PDE is solved by means of arbitrarily selected closure functions. The contracting space is then split into two variables. The compactness of some solutions is enhanced by numerically integrating the contracting domain while retaining a solution for the nonlinear PDE. The validation of numerical schemes is demonstrated for the Euler and Navier-Stokes PDE. As the nonlinear response is isolated in only one spatial dimension, the method permits to validate arbitrary unstructured meshes and domain geometries by introducing the spatial dimension n + 1.

show abstract

The Navier-Stokes system with temperature and salinity for free surface flows. Numerical scheme and validation

Boittin,

Bouchut,

Bristeau

et al. 2024

Journal of Computational Physics

View full text Add to dashboard Cite

Some analytical solutions for validation of free surface flow computational codes

Abstract: Abstract

Cited by 5 publications

References 7 publications

Semi-Analytical Solutions of Shallow Water Waves with Idealised Bottom Topographies

Semi-Analytical Solutions of Shallow Water Waves with Idealised Bottom Topographies

Solitary solution method for incompressible Navier-Stokes PDE

The Navier-Stokes system with temperature and salinity for free surface flows. Numerical scheme and validation

Contact Info

Product

Resources

About