Jean-Paul Caltagirone

Fictitious domain approach for numerical modelling of Navier–Stokes equations

This study investigates a fictitious domain model for the numerical solution of various incompressible viscous flows. It is based on the so-called Navier–Stokes/Brinkman and energy equations with discontinuous coefficients all over an auxiliary embedding domain. The solid obstacles or walls are taken into account by a penalty technique. Some volumic control terms are directly introduced in the governing equations in order to prescribe immersed boundary conditions. The implicit numerical scheme, which uses an upwind finite volume method on staggered Cartesian grids, is of second-order accuracy in time and space. A multigrid local mesh refinement is also implemented, using the multi-level Zoom Flux Interface Correction (FIC) method, in order to increase the precision where it is needed in the domain. At each time step, some iterations of the augmented Lagrangian method combined with a preconditioned Krylov algorithm allow the divergence-free velocity and pressure fields be solved for. The tested cases concern external steady or unsteady flows around a circular cylinder, heated or not, and the channel flow behind a backward-facing step. The numerical results are shown in good agreement with other published numerical or experimental data. Copyright

Efficient solving method for unsteady incompressible interfacial flow problems

Unsteady interfacial problems, considered in an Eulerian form, are studied. The phenomena are modeled using the incompressible viscous Navier-Stokes equations to get the velocity field and an advection equation to predict interface evolutions. The momentum equation is solved by means of an implicit hybrid augmented Lagrangian-Projection method, whereas an explicit characteristic method coupled with a TVD SUPERBEE scheme is applied to the advection equation. The velocity components and the pressure are discretized on staggered grids with finite volumes. Emphasis is on the accuracy and robustness of the techniques described before. A precise explanation on the validation phase will be given, which uses such tests as the advection of a step function or Zalesaks problem to improve the calculation of the interface. The global approach is used on a physically hard interfacial test with strong disparities between viscosities and densities

Thermal diffusion sensitivity to the molecular parameters of a binary equimolar mixture, a non-equilibrium molecular dynamics approach

Abstract The goal of this study is to analyse how the thermal diffusion process is dependent on molecular parameters when describing a fluid mixture. To estimate the associated transport coefficient, which is the thermal diffusion factor αT, a non-equilibrium molecular dynamics algorithm has been applied on equimolar binary mixtures of Lennard–Jones (LJ) particles in supercritical conditions. Firstly, it is shown that this model is able to correctly estimate αT for simple alkane mixtures, provided there are a sufficient number of particles and long enough simulations. Then, using various mixing rules, the separate influences of the mass, the moment of inertia, the atomic diameter and the interaction strength have been studied. Results indicate that the molar fraction of the component, having the smallest mass and moment of inertia as well as the biggest radius and the strongest potential, tends to increase in the hot area. Elsewhere, simulations for various cross-interaction parameters show that αT is extremely sensitive to the intermolecular pair potential between unlike particles. Finally, results on methane/normal alkane mixtures indicate that a simple sum between the separate contributions provides a reliable evaluation of αT only when the molecular parameter ratios between the two components are close to 1.

A NUMERICAL CONTINUOUS MODEL FOR THE HYDRODYNAMICS OF FLUID PARTICLE SYSTEMS

SUMMARY In order to understand the hydrodynamic interactions that can appear in a fluid particle motion, an original method based on the equations governing the motion of two immiscible fluids has been developed. These momentum equations are solved for both the fluid and solid phases. The solid phase is assumed to be a fluid phase with physical properties, such as its behaviour can be assimilated to that of pseudo-rigid particles. The only unknowns are the velocity and the pressure defined in both phases. The unsteady two-dimensional momentum equations are solved by using a staggered finite volume formulation and a projection method. The transport of each particle is solved by using a second-order explicit scheme. The physical model and the numerical method are presented, and the method is validated through experimental measurements and numerical results concerning the flow around a circular cylinder. Good agreement is observed in most cases. The method is then applied to study the trajectory of one settling particle initially off-centred between two parallel walls and the corresponding wake effects. Different particle trajectories related to particulate Reynolds numbers are presented and commented. A two-body interaction problem is investigated too. This method allows the simulation of the transport of particles in a dilute suspension in reasonable time. One of the important features of this method is the computational cost that scales linearly with the number of particles. Copyright

On thermal diffusion in binary and ternary Lennard-Jones mixtures by non-equilibrium molecular dynamics

Molecular simulation appears to be an alternative to experiment for the estimation of transport and thermodynamics properties of fluid mixtures, which is of primary importance in the evaluation of the initial state of a petroleum reservoir. In this study, a non-equilibrium molecular dynamics algorithm has been applied to mixtures of Lennard-Jones spheres in order to compute the thermal diffusion process. The pertinence of such an approach to simple alkane mixtures is shown. The separate influences on the thermal diffusion of the molecular features in binary equimolar mixtures are then summarized. Simulations on binary non-equimolar mixtures have been performed as well. The results indicate an increase in the thermal diffusion process with increasing molar fraction of the lightest component. Moreover, this increase is enhanced with increasing difference in the number of carbons between the two alkanes. Then, a simple method, which yields results consistent with simulations, is proposed to predict thermal diffusion for the whole range of molar fractions starting only from the equimolar value. Finally, for ternary mixtures, the law of the corresponding states is shown to be valid when the appropriate mixing rules are applied, which allows the estimation of thermal diffusion in such mixtures from equivalent binary mixtures.

Augmented Lagrangian and penalty methods for the simulation of two-phase flows interacting with moving solids. Application to hydroplaning flows interacting with real tire tread patterns

The numerical simulation of the interaction between a free surface flow and a moving obstacle is considered for the analysis of hydroplaning flows. A new augmented Lagrangian method, coupled to fictitious domains and penalty methods, is proposed for the simulation of multi-phase flows. The augmented Lagrangian parameter is estimated by an automatic analysis of the discretization matrix resulting from the approximation of the momentum equations. The algebraic automatic augmented Lagrangian 3AL approach is validated on the natural convection in a differentially heated cavity, a two-dimensional collapse of a water column, the three-dimensional settling of a particle in a tank and the falling of a dense cylinder in air. Finally, the 3AL method is utilized to simulate the hydroplaning of a tire under various pattern shape conditions.

Eulerian-Lagrangian multiscale methods for solving scalar equations - Application to incompressible two-phase flows

The present article proposes a new hybrid Eulerian-Lagrangian numerical method, based on a volume particle meshing of the Eulerian grid, for solving transport equations. The approach, called Volume Of Fluid Sub-Mesh method (VOF-SM), has the advantage of being able to deal with interface tracking as well as advection-diffusion transport equations of scalar quantities. The Eulerian evolutions of a scalar field could be obtained on any orthogonal curvilinear grid thanks to the Lagrangian advection and a redistribution of particles on the Eulerian grid. The Eulerian concentrations result from the projection of the volume and scalar informations handled by the particles. The particle velocities are interpolated from the Eulerian velocity field. The VOF-SM method is validated on several scalar interface tracking and transport problems and is compared to existing schemes within the literature. It is finally coupled to a Navier-Stokes solver and applied to the simulation of two free-surface flows, i.e. the two-dimensional buckling of a viscous jet during the filling of a square mold and the three-dimensional dam-break flow in a tank.

A fast vector penalty-projection method for incompressible non-homogeneous or multiphase Navier-Stokes problems

We present a new {\em fast vector penalty-projection method (VPP

A molecular dynamics study of thermal diffusion in a porous medium

_{\eps}

Modelling the interactions between a thermal plasma flow and a continuous liquid jet in a suspension spraying process

)} to efficiently compute the solution of unsteady Navier-Stokes problems governing incompressible multiphase viscous flows with variable density and/or viscosity. The key idea of the method is to compute at each time step an accurate and curl-free approximation of the pressure gradient increment in time. This method performs a {\em two-step approximate divergence-free vector projection} yielding a velocity divergence vanishing as