Modeling Free Surface Flows Using Stabilized Finite Element Method

Deepak Garg,Paolo Papale,Antonella Longo

doi:10.1155/2018/6154251

Deepak Garg, Paolo Papale + Show 1 more

Open Access

https://doi.org/10.1155/2018/6154251

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Abstract

This work aims to develop a numerical wave tank for viscous and inviscid flows. The Navier-Stokes equations are solved by time-discontinuous stabilized space-time finite element method. The numerical scheme tracks the free surface location using fluid velocity. A segregated algorithm is proposed to iteratively couple the fluid flow and mesh deformation problems. The numerical scheme and the developed computer code are validated over three free surface problems: solitary wave propagation, the collision between two counter moving waves, and wave damping in a viscous fluid. The benchmark tests demonstrate that the numerical approach is effective and an attractive tool for simulating viscous and inviscid free surface flows.

Highlights

Numerical simulations of flow with moving boundaries have received a growing interest in last few years. Many engineering applications such as ship hydrodynamics, dam break, sloshing in tanks, shallow water, and mold filling [1,2,3] are modeled with free surface flows
A big disadvantage of these methods is that the level set method captures the free surface accurately but does not conserve the mass whereas the volume of fluid conserves the mass but does not capture the free surface accurately
In Lagrangian, all mesh nodes follow the fluid motion, while in Arbitrary Lagrangian-Eulerian (ALE) method only the boundary nodes move with the fluid velocity and the interior nodes move arbitrarily

Summary

Introduction

Numerical simulations of flow with moving boundaries have received a growing interest in last few years Many engineering applications such as ship hydrodynamics, dam break, sloshing in tanks, shallow water, and mold filling [1,2,3] are modeled with free surface flows. Moving domain problems are modeled with interfacecapturing and interface-tracking techniques In interfacecapturing methods such as the level set [6, 7] and the volume of fluid [8, 9] a fixed grid is used. Our aim in this work is to develop a robust interface-tracking numerical code for simulating viscous and inviscid flows to be used for the natural hazard problems such as the tsunami wave amplification analysis.

Flow Governing Equations

Numerical Scheme

Numerical Examples

Conclusions