Hydraulic Model of Dam Break Using Navier Stokes Equation with Arbitrary Lagrangian-Eulerian Approach

Abstract

 Abstract—The liquid flow and the free surface shape during the initial stage of dam breaking are investigated. A numerical scheme is developed to predict the wave of an unsteady, incompressible viscous flow with free surface. The method involves a two dimensional finite element (2D), in a vertical plan. The Naiver-Stokes equations for conservation of momentum and mass for Newtonian fluids, continuity equation, and full nonlinear kinematic free-surface equation, were used as the governing equations. The mapping developed to solve highly deformed free surface problems common in waves formed during wave propagation, transforms the run up model from the physical domain to a computational domain with Lagrangian Eulerian (ALE) finite element modeling technique. fluid columns of semi-cylindrical and hemispherical shapes, and showed that these asymptotic are not valid close to the base, where the fluid velocity is much higher than in the rest of the column. The numerical solution for free surfaces has been developed using three defined theories: 1) Lagrangian; 2) Eulerian; 3) Lagrangian-Eulerian description. For waves in particular, the Lagrangian-Eulerian is superior in terms of handling high distortion in the grids. To have a versatile description of the fluid domain, it is necessary to have a method with the benefits of both Lagrangian and Eulerian descriptions, without their deficiencies. Such a method, developed in the last two decades, is the Arbitrary Lagrangian- Eulerian formulation in which grid points may be moved with the fluid in normal Lagrangian description. This method allows the grids move independent of the fluid motion.