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 Numerical and Experimental Investigation of Wave Overtopping of Barriers

Water ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 451 ◽  
Author(s):  
Cannata ◽  
Tamburrino ◽  
Ferrari ◽  
Badas ◽  
Querzoli
Keyword(s):  
Free Surface ◽  
Numerical Scheme ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Experimental Tests ◽  
Integral Form ◽  
Breaking Waves ◽  
Free Surface Flows ◽  
Navier Stokes ◽  
Wave Overtopping

We present a study of wave overtopping of barriers. The phenomenon of the wave overtopping over emerged structures is reproduced both numerically and experimentally. The numerical simulations are carried out by a numerical scheme for three-dimensional free-surface flows, which is based on the solution of the Navier–Stokes equations in a novel integral form on a time-dependent coordinate system. In the adopted numerical scheme, a novel wet–dry technique, based on the exact solution of the Riemann problem over the dry bed, is proposed. The experimental tests are carried out by adopting a nonintrusive and continuous-in-space image-analysis technique, which is able to properly identify the free surface even in very shallow waters or breaking waves. A comparison between numerical and experimental results, for several wave and water-depth conditions, is shown.

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.

Numerical Modeling of Flow Over a Dam Spillway

2006 ◽  
Author(s):  
Iraj Saeedpanah ◽  
M. Shayanfar ◽  
E. Jabbari ◽  
Mohammad Haji Mohammadi
Keyword(s):  
Free Surface ◽  
Stokes Equations ◽  
Iterative Solution ◽  
Free Surface Flows ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Continuity Equations ◽  
Water Jets ◽  
Pressure Fields ◽  
Good Agreement

Free surface flows are frequently encountered in hydraulic engineering problems including water jets, weirs and around gates. An iterative solution to the incompressible two-dimensional vertical steady Navier-Stokes equations, comprising momentum and continuity equations, is used to solve for the priori unknown free surface, the velocity and the pressure fields. The entire water body is covered by a unstructured finite element grid which is locally refined. The dynamic boundary condition is imposed for the free surface where the pressure vanishes. This procedure is done continuously until the normal velocities components vanish. To overcome numerical errors and oscillations encountering in convection terms, the SUPG (streamline upwinding Petrov-Galerkin) method is applied. The solution method is tested for different discharges onto a standard spillway geometries. The results shows good agreement with available experimental data.

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.

Application of a generalized finite difference method to mould filling process

2017 ◽  
Vol 29 (3) ◽  
pp. 450-469 ◽  
Author(s):  
E. O. RESÉNDIZ-FLORES ◽  
J. KUHNERT ◽  
F. R. SAUCEDO-ZENDEJO
Keyword(s):  
Free Surface ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Stokes Equations ◽  
Free Surface Flows ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Filling Process ◽  
Mould Filling

This paper proposes the use of a generalized finite difference method for the numerical simulation of free surface single phase flows during mould filling process which are common in some industrial processes particularly in the area of metal casting. A novel and efficient idea for the computation of the normal vectors for free surface flows is introduced and presented for the first time. The incompressible Navier–Stokes equations are numerically solved by the well-known Chorin's projection method. After we showed the main ideas behind the meshless approach, some numerical results in two and three dimensions are presented corresponding to mould filling process simulation.

Numerical and asymptotic methods for certain viscous free-surface flows

1992 ◽  
Vol 340 (1656) ◽  
pp. 1-45 ◽  
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Free Surface Flows ◽  
Navier Stokes ◽  
Lubrication Approximation ◽  
Navier Stokes Equations ◽  
Flow Rates

This paper concerns the two-dimensional motion of a viscous liquid down a perturbed inclined plane under the influence of gravity, and the main goal is the prediction of the surface height as the fluid flows over the perturbations. The specific perturbations chosen for the present study were two humps stretching laterally across an otherwise uniform plane, with the flow being confined in the lateral direction by the walls of a channel. Theoretical predictions of the flow have been obtained by finite-element approximations to the Navier-Stokes equations and also by a variety of lubrication approximations. The predictions from the various models are compared with experimental measurements of the free-surface profiles. The principal aim of this study is the establishment and assessment of certain numerical and asymptotic models for the description of a class of free-surface flows, exemplified by the particular case of flow over a perturbed inclined plane. The laboratory experiments were made over a range of flow rates such that the Reynolds number, based on the volume flux per unit width and the kinematical viscosity of the fluid, ranged between 0.369 and 36.6. It was found that, at the smaller Reynolds numbers, a standard lubrication approximation provided a very good representation of the experimental measurements but, as the flow rate was increased, the standard model did not capture several important features of the flow. On the other hand, a lubrication approximation allowing for surface tension and inertial effects expanded the range of applicability of the basic theory by almost an order of magnitude, up to Reynolds numbers approaching 10. At larger flow rates, numerical solutions to the full equations of motion provided a description of the experimental results to within about 4% , up to a Reynolds number of 25, beyond which we were unable to obtain numerical solutions. It is not known why numerical solutions were not possible at larger flow rates, but it is possible that there is a bifurcation of the Navier-Stokes equations to a branch of unsteady motions near a Reynolds number of 25.

Validation Study for Free-Surface Wave Flows Around Surface-Piercing Cylindrical Structures

2005 ◽  
Author(s):  
Shin Hyung Rhee ◽  
Boris Makarov
Keyword(s):  
Free Surface ◽  
Surface Wave ◽  
Breaking Waves ◽  
Navier Stokes ◽  
Test Cases ◽  
Ship Waves ◽  
Cylindrical Structures ◽  
Free Surface Waves ◽  
Free Surface Wave ◽  
Wave Flows

The present study is concerned with the free-surface wave flows around surface-piercing cylindrical structures. The volume of fluid method implemented in a Navier-Stokes computational fluid dynamics code is employed for test cases that involve general ship waves, spilling breaking waves, bubbly free-surface in separated regions, and interaction between free-surface waves and underlying viscous flow. The computational results are validated against existing experimental data, showing good agreement. The validation results suggest that the present computational approach provides a tool that is flexible and accurate enough to capture the outstanding flow physics associated with the free-surface wave flows around surface-piercing cylindrical structures.

scholarly journals A SEMI-IMPLICIT SCHEME FOR SOLVING INCOMPRESSIBLE VISCOUS FREE SURFACE FLOWS

2005 ◽  
Vol 4 (2) ◽  
Author(s):  
C. M. Oishi ◽  
J. A. Cuminato ◽  
V. G. Ferreira ◽  
M. F. Tomé ◽  
A. Castelo ◽  
...  
Keyword(s):  
Free Surface ◽  
Numerical Method ◽  
Stokes Equations ◽  
Free Surface Flows ◽  
Numerical Results ◽  
Navier Stokes ◽  
Variable Order ◽  
Navier Stokes Equations ◽  
Reynolds Number Flow ◽  
The Stability

The present work is concerned with a numerical method for solving the two-dimensional time-dependent incompressible Navier-Stokes equations in the primitive variables formulation. The diffusive terms are treated by Implicit Backward and Crank-Nicolson methods, and the non-linear convection terms are, explicitly, approximated by the high order upwind VONOS (Variable-Order Non-Oscillatory Scheme) scheme. The boundary conditions for the pressure field at the free surface are treated implicitly, and for the velocity field explicitly. The numerical method is then applied to the simulation of free surface and confined flows. The numerical results show that the present technique eliminates the stability restriction in the original explicit method. For low Reynolds number flow dynamics, the method is robust and produces numerical results that compare very well with the analytical solutions.

scholarly journals A SEMI-IMPLICIT SCHEME FOR SOLVING INCOMPRESSIBLE VISCOUS FREE SURFACE FLOWS

2005 ◽  
Vol 4 (2) ◽  
pp. 106
Author(s):  
C. M. Oishi ◽  
J. A. Cuminato ◽  
V. G. Ferreira ◽  
M. F. Tomé ◽  
A. Castelo ◽  
...  
Keyword(s):  
Free Surface ◽  
Numerical Method ◽  
Stokes Equations ◽  
Free Surface Flows ◽  
Numerical Results ◽  
Navier Stokes ◽  
Variable Order ◽  
Navier Stokes Equations ◽  
Reynolds Number Flow ◽  
The Stability

The present work is concerned with a numerical method for solving the two-dimensional time-dependent incompressible Navier-Stokes equations in the primitive variables formulation. The diffusive terms are treated by Implicit Backward and Crank-Nicolson methods, and the non-linear convection terms are, explicitly, approximated by the high order upwind VONOS (Variable-Order Non-Oscillatory Scheme) scheme. The boundary conditions for the pressure field at the free surface are treated implicitly, and for the velocity field explicitly. The numerical method is then applied to the simulation of free surface and confined flows. The numerical results show that the present technique eliminates the stability restriction in the original explicit method. For low Reynolds number flow dynamics, the method is robust and produces numerical results that compare very well with the analytical solutions.

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