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# Predicting Wave Run-Up using Full ALE Finite Element Approach considering Moving Boundary

Shahin Zohouri1, Moharram D. Pirooz2, Asad Esmaeily3
PHD. Graduate, Department of Civil Engineering, University of Tehran, Tehran, Iran, Tel:+98-261-350 2496, E-mail: szohouri@ut.ac.ir
Assistant Professor, Department of Civil Engineering, University of Tehran, Tehran, Iran, Tel: +98-21-611 3294, E-mail: mdolat@ut.ac.ir
Assistant Professor, Department of Civil Engineering, Kansas State University, Fiedler Hall 2118, Manhattan, KS 66506-2905, Tel:(785)- 532 6063, Fax:(785)- 532 7717, E-mail: asad@ksu.edu

Computer Modeling in Engineering & Sciences 2005, 7(1), 107-118. https://doi.org/10.3970/cmes.2005.007.107

### Abstract

A numerical scheme is developed to predict the wave run-up of an unsteady, incompressible viscous flow with free surface by the author\$^1\$. The method involves a two dimensional finite element with moving boundaries. The governing equations were the Navier-Stokes equations for conservation of momentum and mass for Newtonian fluids, continuity equation, and full nonlinear kinematic free-surface equation. A mapping algorithm was developed to solve highly deformed free surface problems, common in wave propagation. This algorithm transforms the run up model from the physical domain to a computational domain. A new Arbitrary Lagrangian-Eulerian (ALE) finite element modeling technique was used to model the fluid flow and predict the wave modification. Oscillation of the surface profile near the vertical wall was corrected by using a numerical procedure in the mapping function, and also by employing moving boundary technique at the wall point where run up happens. These oscillations are associated with mapping process at the boundaries when a full ALE finite element approach is used in both coordinate directions.

### Keywords

Wave run-up, finite element, free surface, conformal mapping, ALE, moving boundary.

Zohouri, S., Pirooz, M. D., Esmaeily, A. (2005). Predicting Wave Run-Up using Full ALE Finite Element Approach considering Moving Boundary. CMES-Computer Modeling in Engineering & Sciences, 7(1), 107–118.

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