scholarly journals Lagrangian vs. Eulerian: An Analysis of Two Solution Methods for Free-Surface Flows and Fluid Solid Interaction Problems

Fluids ◽  
2021 ◽  
Vol 6 (12) ◽  
pp. 460
Author(s):  
Milad Rakhsha ◽  
Christopher E. Kees ◽  
Dan Negrut
Keyword(s):  
Free Surface ◽  
Stokes Equations ◽  
Free Surface Flows ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Surface Flows ◽  
Flow Around Cylinder ◽  
Solution Methods ◽  
Particle Hydrodynamics ◽  
Fluid Solid Interaction

As a step towards addressing a scarcity of references on this topic, we compared the Eulerian and Lagrangian Computational Fluid Dynamics (CFD) approaches for the solution of free-surface and Fluid–Solid Interaction (FSI) problems. The Eulerian approach uses the Finite Element Method (FEM) to spatially discretize the Navier–Stokes equations. The free surface is handled via the volume-of-fluid (VOF) and the level-set (LS) equations; an Immersed Boundary Method (IBM) in conjunction with the Nitsche’s technique were applied to resolve the fluid–solid coupling. For the Lagrangian approach, the smoothed particle hydrodynamics (SPH) method is the meshless discretization technique of choice; no additional equations are needed to handle free-surface or FSI coupling. We compared the two approaches for a flow around cylinder. The dam break test was used to gauge the performance for free-surface flows. Lastly, the two approaches were compared on two FSI problems—one with a floating rigid body dropped into the fluid and one with an elastic gate interacting with the flow. We conclude with a discussion of the robustness, ease of model setup, and versatility of the two approaches. The Eulerian and Lagrangian solvers used in this study are open-source and available in the public domain.

Modélisation tridimensionnelle de l'écoulement au voisinage d'un aménagement portuaire

1989 ◽  
Vol 16 (6) ◽  
pp. 829-844
Author(s):  
A. Soulaïmani ◽  
Y. Ouellet ◽  
G. Dhatt ◽  
R. Blanchet
Keyword(s):  
Free Surface ◽  
Computational Analysis ◽  
Stokes Equations ◽  
A Priori ◽  
Three Dimensional ◽  
Free Surface Flows ◽  
Solution Algorithm ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Surface Flows

This paper is devoted to the computational analysis of three-dimensional free surface flows. The model solves the Navier-Stokes equations without any a priori restriction on the pressure distribution. The variational formulation along with the solution algorithm are presented. Finally, the model is used to study the hydrodynamic regime in the vicinity of a projected harbor installation. Key words: free surface flows, three-dimensional flows, finite element method.

Numerical Simulation of Transient Free Surface Flows Using a Moving Mesh Technique

2006 ◽  
Vol 73 (6) ◽  
pp. 1017-1025 ◽  
Author(s):  
Laura Battaglia ◽  
Jorge D’Elía ◽  
Mario Storti ◽  
Norberto Nigro
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Incompressible Flow ◽  
Stokes Equations ◽  
Free Surface Flows ◽  
Navier Stokes ◽  
Time Step ◽  
Surface Flows ◽  
Flow Domain ◽  
Convection Dominated

In this work, transient free surface flows of a viscous incompressible fluid are numerically solved through parallel computation. Transient free surface flows are boundary-value problems of the moving type that involve geometrical nonlinearities. In contrast to more conventional computational fluid dynamics problems, the computational flow domain is partially bounded by a free surface which is not known a priori, since its shape must be computed as part of the solution. In steady flow the free surface is obtained by an iterative process, but when the free surface evolves with time the problem is more difficult as it generates large distortions in the computational flow domain. The incompressible Navier-Stokes numerical solver is based on the finite element method with equal order elements for pressure and velocity (linear elements), and it uses a streamline upwind/Petrov-Galerkin (SUPG) scheme (Hughes, T. J. R., and Brooks, A. N., 1979, “A Multidimensional Upwind Scheme With no Crosswind Diffusion,” in Finite Element Methods for Convection Dominated Flows, ASME ed., 34. AMD, New York, pp. 19–35, and Brooks, A. N., and Hughes, T. J. R., 1982, “Streamline Upwind/Petrov-Galerkin Formulations for Convection Dominated Flows With Particular Emphasis on the Incompressible Navier-Stokes Equations,” Comput. Methods Appl. Mech. Eng., 32, pp. 199–259) combined with a Pressure-Stabilizing/Petrov-Galerkin (PSPG) one (Tezduyar, T. E., 1992, “Stablized Finite Element Formulations for Incompressible Flow Computations,” Adv. Appl. Mech., 28, pp. 1–44, and Tezduyar, T. E., Mittal, S., Ray, S. E., and Shih, R., 1992, “Incompressible Flow Computations With Stabilized Bilinear and Linear Equal Order Interpolation Velocity-Pressure Elements,” Comput. Methods Appl. Mech. Eng., 95, pp. 221–242). At each time step, the fluid equations are solved with constant pressure and null viscous traction conditions at the free surface and the velocities obtained in this way are used for updating the positions of the surface nodes. Then, a pseudo elastic problem is solved in the fluid domain in order to relocate the interior nodes so as to keep mesh distortion controlled. This has been implemented in the PETSc-FEM code (PETSc-FEM: a general purpose, parallel, multi-physics FEM program. GNU general public license (GPL), http://www.cimec.org.ar/petscfem) by running two parallel instances of the code and exchanging information between them. Some numerical examples are presented.

A Study of Multi-Step Overfall Flows by Computational Fluid Dynamics

2013 ◽  
Vol 405-408 ◽  
pp. 3208-3212
Author(s):  
Jyh Haw Tang ◽  
Ming Kuan Sun ◽  
Ying Chen
Keyword(s):  
Free Surface ◽  
Stokes Equations ◽  
Surface Profile ◽  
Free Surface Flows ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Surface Flows ◽  
Engineering Designs ◽  
Free Surface Profile ◽  
Free Overfall

This paper proposes the least-squares finite element method (LSFEM) for simulating the free surface flows in multi-step free overfalls. Motion of the free surface flows is represented with two-phased surface profiles by solving the Navier-Stokes equations. The fluid is considered to be incompressible and the dynamic and kinematic boundary conditions of free surface are described in an Eulerian coordinate system. In this simulation, the volume of fluid (VOF) method and continuous stress force (CSF) models in association of color function are incorporated for the determination of the interface between water and air. The simulation results from the LSFEM model are carefully verified for the unit-step free overfall case. The quantitative comparisons in terms of the parameters such as different inflow rates, reattached length, water height after the fall and critical depth with previous numerical results or experimental measurements are shown to be in good agreement. In order to understand more about the complicate free surface profile of a dual-step free overfall, the LSFEM model is simulated for different inflow rates. In comparison with the available experimental data, it is shown that the LSFEM can effectively simulate the multi-step free overfall flow phenomena. Our study presents some regression formula for the dual-step free overfall, it is hoped that these formula will be helpful for the engineering designs and applications.

The Application of Numerical Methods for the Solution of Some Problems in Free-Surface Hydrodynamics

2005 ◽  
Vol 49 (04) ◽  
pp. 288-301
Author(s):  
U. P. Bulgarelli
Keyword(s):  
Free Surface ◽  
Numerical Methods ◽  
Stokes Equations ◽  
Level Set Methods ◽  
Breaking Waves ◽  
Free Surface Flows ◽  
Navier Stokes ◽  
Robust Algorithms ◽  
Ship Waves ◽  
Particle Hydrodynamics

The aim of this contribution is to present some of the recent developments achieved at INSEAN in the context of accurate and robust algorithms for the solutions of the system of partial differential equations governing complex free-surface flows. The paper addresses several problems of relevant interest in naval hydrodynamics, for example, sloshing, water on deck, microscale breaking waves, bow-stern flows, ship waves, steady and unsteady ship flows. Each problem is solved through the most appropriate numerical method, which is selected on the basis of the approximations that can be done for the particular problem and of the kind of result that the analysis has to provide. Numerical methods adopted involve classical boundary element approaches, smoothed particle hydrodynamics, heterogeneous domain decomposition techniques, level-set methods, steady and unsteady Reynolds averaged Navier-Stokes equations. Validation versus experimental data are presented. Comparisons among different numerical approaches are also established in a few cases with the aim of highlighting their limits and/or capabilities.

scholarly journals Modeling Free Surface Flows Using Stabilized Finite Element Method

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Deepak Garg ◽  
Antonella Longo ◽  
Paolo Papale
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Surface ◽  
Numerical Scheme ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Computer Code ◽  
Free Surface Flows ◽  
Surface Flows ◽  
Element Method

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.

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