TY - JOUR

T1 - An arbitrary Lagrangian-Eulerian finite element method for solving three-dimensional free surface flows

AU - Soulaimani, Azzeddine

AU - Saad, Yousef

N1 - Funding Information:
work was supportedbya Hydro-Quebec contract and grants from NSERC of Canada, NASA

PY - 1998/8/25

Y1 - 1998/8/25

N2 - This paper discusses numerical solution of unsteady three-dimensional free surface flows. The governing equilibrium equations are written in the framework of the Arbitrary Lagrangian-Eulerian kinematic description. The corresponding variational formulation is established afterwards. Since the variational problems are nonlinear with respect to the moving coordinates, a second-order approximate variational problem is derived after a consistent linearization of the referential motion. Stability of the discrete formulations is ensured with the help of a new stabilization method. A robust preconditioned GMRES algorithm is then used to solve the resulting set of nonlinear equations. Finally, the computational algorithms are assessed through numerical studies of various problems: a large sloshing flow in a three-dimensional reservoir, a discharge flow from a reservoir, simulation of a liquid vortex produced inside a cylindrical container with a disk rotating at the bottom and a three-dimensional practical hydraulic problem.

AB - This paper discusses numerical solution of unsteady three-dimensional free surface flows. The governing equilibrium equations are written in the framework of the Arbitrary Lagrangian-Eulerian kinematic description. The corresponding variational formulation is established afterwards. Since the variational problems are nonlinear with respect to the moving coordinates, a second-order approximate variational problem is derived after a consistent linearization of the referential motion. Stability of the discrete formulations is ensured with the help of a new stabilization method. A robust preconditioned GMRES algorithm is then used to solve the resulting set of nonlinear equations. Finally, the computational algorithms are assessed through numerical studies of various problems: a large sloshing flow in a three-dimensional reservoir, a discharge flow from a reservoir, simulation of a liquid vortex produced inside a cylindrical container with a disk rotating at the bottom and a three-dimensional practical hydraulic problem.

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U2 - 10.1016/S0045-7825(97)00330-7

DO - 10.1016/S0045-7825(97)00330-7

M3 - Article

AN - SCOPUS:0032566424

SN - 0374-2830

VL - 162

SP - 79

EP - 106

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

IS - 1-4

ER -