A semi-Lagrangian level set method for incompressible Navier-Stokes equations with free surface

2005 ◽  
Vol 49 (10) ◽  
pp. 1111-1146 ◽  
Author(s):  
Leo Miguel González Gutiérrez ◽  
Rodolfo Bermejo
Keyword(s):  
Free Surface ◽  
Level Set Method ◽  
Level Set ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

Simulation of Wave-Body Interaction Using a Single-Phase Level Set Function in the SWENSE Method

2013 ◽  
Author(s):  
Gabriel Reliquet ◽  
Aurélien Drouet ◽  
Pierre-Emmanuel Guillerm ◽  
Erwan Jacquin ◽  
Lionel Gentaz ◽  
...  
Keyword(s):  
Free Surface ◽  
Level Set Method ◽  
Level Set ◽  
Single Phase ◽  
Stokes Equations ◽  
Flow Theory ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Level Set Function ◽  
Set Function

The purpose of this paper is to present combination of the SWENSE (Spectral Wave Explicit Navier-Stokes Equations – [1]) method — an original method to treat fully nonlinear wave-body interactions — and a free surface RANSE (Reynolds Averaged Navier-Stokes Equations) solver using a single-phase Level Set method to capture the interface. The idea is to be able to simulate wave-body interactions under viscous flow theory with strong deformations of the interface (wave breaking in the vicinity of the body, green water on ship decks…), while keeping the advantages of the SWENSE scheme. The SWENSE approach is based on a physical decomposition by combining incident waves described by a nonlinear spectral scheme based on potential flow theory and an adapted Navier-Stokes solver where only the diffracted part of the flow is solved, incident flow parameters seen as forcing terms. In the single-phase Level Set method [2, 3], the air phase is neglected. Thus, only the liquid phase is solved considering a fluid with uniform properties. The location of the free surface is determined by a Level Set function initialised as the signed distance. The accuracy of simulation depends essentially on the pressure scheme used to impose free surface dynamic boundary condition. Comparisons of numerical results with experimental and numerical data for US navy combatant DTMB 5415 in calm water and in head waves are presented.

Level-Set Computations of Free Surface Rotational Flows

2005 ◽  
Vol 127 (6) ◽  
pp. 1111-1121 ◽  
Author(s):  
Giuseppina Colicchio ◽  
Maurizio Landrini ◽  
John R. Chaplin
Keyword(s):  
Free Surface ◽  
Numerical Method ◽  
Level Set ◽  
Stokes Equations ◽  
Vertical Surface ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Two Fluids ◽  
Level Set Function ◽  
Rotational Flows

A numerical method is developed for modeling the violent motion and fragmentation of an interface between two fluids. The flow field is described through the solution of the Navier-Stokes equations for both fluids (in this case water and air), and the interface is captured by a Level-Set function. Particular attention is given to modeling the interface, where most of the numerical approximations are made. Novel features are that the reintialization procedure has been redefined in cells crossed by the interface; the density has been smoothed across the interface using an exponential function to obtain an equally stiff variation of the density and of its inverse; and we have used an essentially non-oscillatory scheme with a limiter whose coefficients depend on the distance function at the interface. The results of the refined scheme have been compared with those of the basic scheme and with other numerical solvers, with favorable results. Besides the case of the vertical surface-piercing plate (for which new laboratory measurements were carried out) the numerical method is applied to problems involving a dam-break and wall-impact, the interaction of a vortex with a free surface, and the deformation of a cylindrical bubble. Promising agreement with other sources of data is found in every case.

scholarly journals Numerical Modeling of the Motion and Interaction of a Droplet of an Inkjet Printing Process with a Flat Surface

2021 ◽  
Vol 11 (2) ◽  
pp. 527
Author(s):  
Tim Tofan ◽  
Harald Kruggel-Emden ◽  
Vytautas Turla ◽  
Raimondas Jasevičius
Keyword(s):  
Level Set ◽  
Stokes Equations ◽  
Field Method ◽  
Phase Field Method ◽  
Navier Stokes ◽  
Stable Form ◽  
Fluid Interface ◽  
Velocity Change ◽  
Navier Stokes Equations ◽  
Inkjet Printhead

The numerical simulation and analysis of the ejection of an ink droplet through a nozzle as well its motion through air until its contact with a surface and taking up of a stable form is performed. The fluid flow is modeled by the incompressible Navier–Stokes equations with added surface tension. The presented model can be solved using either a level set or a phase field method to track the fluid interface. Here, the level set method is used to determinate the interface between ink and air. The presented work concentrates on the demonstration how to check the suitability of ink for inkjet printhead nozzles, for instance, for the use in printers. The results such as velocity, change of size, and volume dependence on time of an ink droplet are presented. Recommendations for the use of specific inks are also given.

Simulation of the Gap Resonance Between Two Rectangular Barges in Regular Waves by a Free Surface Viscous Flow Solver

2013 ◽  
Author(s):  
B. Elie ◽  
G. Reliquet ◽  
P.-E. Guillerm ◽  
O. Thilleul ◽  
P. Ferrant ◽  
...  
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Viscous Flow ◽  
Stokes Equations ◽  
Resonance Phenomenon ◽  
Navier Stokes ◽  
Regular Waves ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Gap Resonance

This paper compares numerical and experimental results in the study of the resonance phenomenon which appears between two side-by-side fixed barges for different sea-states. Simulations were performed using SWENSE (Spectral Wave Explicit Navier-Stokes Equations) approach and results are compared with experimental data on two fixed barges with different headings and bilges. Numerical results, obtained using the SWENSE approach, are able to predict both the frequency and the magnitude of the RAO functions.

NUMERICAL SOLUTIONS OF 2D AND 3D SLAMMING PROBLEMS

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
Q Yang ◽  
W Qiu
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Type Equation ◽  
The Body ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Highly Nonlinear ◽  
2D And 3D

Slamming forces on 2D and 3D bodies have been computed based on a CIP method. The highly nonlinear water entry problem governed by the Navier-Stokes equations was solved by a CIP based finite difference method on a fixed Cartesian grid. In the computation, a compact upwind scheme was employed for the advection calculations and a pressure-based algorithm was applied to treat the multiple phases. The free surface and the body boundaries were captured using density functions. For the pressure calculation, a Poisson-type equation was solved at each time step by the conjugate gradient iterative method. Validation studies were carried out for 2D wedges with various deadrise angles ranging from 0 to 60 degrees at constant vertical velocity. In the cases of wedges with small deadrise angles, the compressibility of air between the bottom of the wedge and the free surface was modelled. Studies were also extended to 3D bodies, such as a sphere, a cylinder and a catamaran, entering calm water. Computed pressures, free surface elevations and hydrodynamic forces were compared with experimental data and the numerical solutions by other methods.

A Cartesian Explicit Solver for Complex Hydrodynamic Applications

2014 ◽  
Author(s):  
P. Bigay ◽  
A. Bardin ◽  
G. Oger ◽  
D. Le Touzé
Keyword(s):  
Level Set ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Simulation Method ◽  
Navier Stokes ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Eddy Simulation ◽  
Flow Past A Cylinder ◽  
Explicit Solver

In order to efficiently address complex problems in hydrodynamics, the advances in the development of a new method are presented here. This method aims at finding a good compromise between computational efficiency, accuracy, and easy handling of complex geometries. The chosen method is an Explicit Cartesian Finite Volume method for Hydrodynamics (ECFVH) based on a compressible (hyperbolic) solver, with a ghost-cell method for geometry handling and a Level-set method for the treatment of biphase-flows. The explicit nature of the solver is obtained through a weakly-compressible approach chosen to simulate nearly-incompressible flows. The explicit cell-centered resolution allows for an efficient solving of very large simulations together with a straightforward handling of multi-physics. A characteristic flux method for solving the hyperbolic part of the Navier-Stokes equations is used. The treatment of arbitrary geometries is addressed in the hyperbolic and viscous framework. Viscous effects are computed via a finite difference computation of viscous fluxes and turbulent effects are addressed via a Large-Eddy Simulation method (LES). The Level-Set solver used to handle biphase flows is also presented. The solver is validated on 2-D test cases (flow past a cylinder, 2-D dam break) and future improvements are discussed.

scholarly journals Linear pulse structure and signalling in a film flow on an inclined plane

1999 ◽  
Vol 396 ◽  
pp. 37-71 ◽  
Author(s):  
LEONID BREVDO ◽  
PATRICE LAURE ◽  
FREDERIC DIAS ◽  
THOMAS J. BRIDGES
Keyword(s):  
Free Surface ◽  
Saddle Point ◽  
Convective Instability ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Results ◽  
Navier Stokes ◽  
Surface Boundary ◽  
Navier Stokes Equations ◽  
Surface Boundary Conditions

The film flow down an inclined plane has several features that make it an interesting prototype for studying transition in a shear flow: the basic parallel state is an exact explicit solution of the Navier–Stokes equations; the experimentally observed transition of this flow shows many properties in common with boundary-layer transition; and it has a free surface, leading to more than one class of modes. In this paper, unstable wavepackets – associated with the full Navier–Stokes equations with viscous free-surface boundary conditions – are analysed by using the formalism of absolute and convective instabilities based on the exact Briggs collision criterion for multiple k-roots of D(k, ω) = 0; where k is a wavenumber, ω is a frequency and D(k, ω) is the dispersion relation function.The main results of this paper are threefold. First, we work with the full Navier–Stokes equations with viscous free-surface boundary conditions, rather than a model partial differential equation, and, guided by experiments, explore a large region of the parameter space to see if absolute instability – as predicted by some model equations – is possible. Secondly, our numerical results find only convective instability, in complete agreement with experiments. Thirdly, we find a curious saddle-point bifurcation which affects dramatically the interpretation of the convective instability. This is the first finding of this type of bifurcation in a fluids problem and it may have implications for the analysis of wavepackets in other flows, in particular for three-dimensional instabilities. The numerical results of the wavepacket analysis compare well with the available experimental data, confirming the importance of convective instability for this problem.The numerical results on the position of a dominant saddle point obtained by using the exact collision criterion are also compared to the results based on a steepest-descent method coupled with a continuation procedure for tracking convective instability that until now was considered as reliable. While for two-dimensional instabilities a numerical implementation of the collision criterion is readily available, the only existing numerical procedure for studying three-dimensional wavepackets is based on the tracking technique. For the present flow, the comparison shows a failure of the tracking treatment to recover a subinterval of the interval of unstable ray velocities V whose length constitutes 29% of the length of the entire unstable interval of V. The failure occurs due to a bifurcation of the saddle point, where V is a bifurcation parameter. We argue that this bifurcation of unstable ray velocities should be observable in experiments because of the abrupt increase by a factor of about 5.3 of the wavelength across the wavepacket associated with the appearance of the bifurcating branch. Further implications for experiments including the effect on spatial amplification rate are also discussed.

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