Some analytical solutions for validation of free surface flow computational codes

Marie-Odile Bristeau (1) , Bernard Di Martino (1) , Anne Mangeney (2) , Jacques Sainte-Marie (1) , Fabien Souillé (1)

1 ANGE - Numerical Analysis, Geophysics and Ecology
2 IPGP (UMR_7154) - Institut de Physique du Globe de Paris

We present several time dependent analytical solutions for the incompressible Euler system with free surface. These analytical solutions give quantitative descriptions of some physical phenomena, such as water motion or waves on space variable topography, and can be used as reference solutions when validating numerical simulation codes. They concern fluid flows governed by Euler equations with or without hydrostatic hypothesis including wet/dry interface, variable density and wide variety of boundary conditions.

Mots clés: River dynamics; Free surface Euler equations; Analytical solutions

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]; Mécanique des fluides [physics.class-ph]

Marie-Odile Bristeau, Bernard Di Martino, Anne Mangeney, Jacques Sainte-Marie, Fabien Souillé. Some analytical solutions for validation of free surface flow computational codes. Journal of Fluid Mechanics, 2021, Journal of Fluid Mechanics, 913 (A17), ⟨10.1017/jfm.2020.1179⟩. ⟨hal-01831622v3⟩