arXiv subjects

R. Scardovelli

Publications and source records attributed to R. Scardovelli.

4 recordsLinked to original sources

arXiv2021

A mass-momentum consistent, Volume-of-Fluid method for incompressible flow on staggered grids

The computation of flows with large density contrasts is notoriously difficult. To alleviate the difficulty we consider a discretization of the Navier-Stokes equation that advects mass and momentum in a consistent manner. Incompressible flow with capillary forces is modeled and the discretization is performed on a staggered grid of Marker and Cell type. The Volume-of-Fluid method is used to track the interface and a Height-Function method is used to compute surface tension. The advection of the volume fraction is performed using either the Lagrangian-Explicit / CIAM (Calcul d'Interface Affine par Morceaux) method or the Weymouth and Yue (WY) Eulerian-Implicit method. The WY method conserves fluid mass to machine accuracy provided incompressibility is satisfied. To improve the stability of these methods momentum fluxes are advected in a manner "consistent" with the volume-fraction fluxes, that is a discontinuity of the momentum is advected at the same speed as a discontinuity of the density. To find the density on the staggered cells on which the velocity is centered, an auxiliary reconstruction of the density is performed. The method is tested for a droplet without surface tension in uniform flow, for a droplet suddenly accelerated in a carrying gas at rest at very large density ratio without viscosity or surface tension, for the Kelvin-Helmholtz instability, for a 3mm-diameter falling raindrop and for an atomizing flow in air-water conditions.

physics.comp-ph↗

arXiv2020

PArallel, Robust, Interface Simulator (PARIS)

Paris (PArallel, Robust, Interface Simulator) is a finite volume code for simulations of immiscible multifluid or multiphase flows. It is based on the "one-fluid" formulation of the Navier-Stokes equations where different fluids are treated as one material with variable properties, and surface tension is added as a singular interface force. The fluid equations are solved on a regular structured staggered grid using an explicit projection method with a first-order or second-order time integration scheme. The interface separating the different fluids is tracked by a Front-Tracking (FT) method, where the interface is represented by connected marker points, or by a Volume-of-Fluid (VOF) method, where the marker function is advected directly on the fixed grid. Paris is written in Fortran95/2002 and parallelized using MPI and domain decomposition. It is based on several earlier FT or VOF codes such as Ftc3D, Surfer or Gerris. These codes and similar ones, as well as Paris, have been used to simulate a wide range of multifluid and multiphase flows.

physics.comp-ph↗

arXiv2018

Transition in a numerical model of contact line dynamics and forced dewetting

We investigate the transition to a Landau-Levich-Derjaguin film in forced dewetting using a quadtree adaptive solution to the Navier-Stokes equations with surface tension. We use a discretization of the capillary forces near the receding contact line that yields an equilibrium for a specified contact angle $θ_Δ$ called the numerical contact angle. Despite the well-known contact line singularity, dynamic simulations can proceed without any explicit additional numerical procedure. We investigate angles from $15^\circ$ to $110^\circ$ and capillary numbers from $0.00085$ to $0.2$ where the mesh size $Δ$ is varied in the range of $0.0035$ to $0.06$ of the capillary length $l_c$. To interpret the results, we use Cox's theory which involves a microscopic distance $r_m$ and a microscopic angle $θ_e$. In the numerical case, the equivalent of $θ_e$ is the angle $θ_Δ$ and we find that Cox's theory also applies. We introduce the scaling factor or gauge function $ϕ$ so that $r_m = Δ/ϕ$ and estimate this gauge function by comparing our numerics to Cox's theory. The comparison provides a direct assessment of the agreement of the numerics with Cox's theory and reveals a critical feature of the numerical treatment of contact line dynamics: agreement is poor at small angles while it is better at large angles. This scaling factor is shown to depend only on $θ_Δ$ and the viscosity ratio $q$. In the case of small $θ_e$, we use the prediction by Eggers [Phys. Rev. Lett., vol. 93, pp 094502, 2004] of the critical capillary number for the Landau-Levich-Derjaguin forced dewetting transition. We generalize this prediction to large $θ_e$ and arbitrary $q$ and express the critical capillary number as a function of $θ_e$ and $r_m$. An analogy can be drawn between $r_m$ and the numerical slip length.

physics.flu-dyn↗

arXiv2017

Direct Numerical Simulations of pore competition in idealized micro-spall using the VOF method

Under shock loading, metals have been found to melt and with reflection of the shock wave from the material free surface, cavities nucleate and grow. This process is referred to as micro spall and has been studied experimentally with analytical models describing debris sizes. Measurements during the cavity growth phase are not possible at present and we present here the Direct Numerical Simulation of an idealized problem where we assume an inviscid, incompressible liquid subject to a constant expansion rate with cavities at a vanishing vapour pressure. In order to allow for a time-varying gas volume a free-surface interface condition has been implemented in an existing incompressible multiphase Navier-Stokes solver, PARIS Simulator, using a volume-of-fluid method. The gas flow remains unsolved and is instead assumed to have a fixed pressure which is applied to the liquid through a Dirichlet boundary condition on the arbitrary liquid-gas interface. Gas bubbles are tracked individually, allowing the gas pressure to be prescribed using a suitable equation of state. Simulations with hundreds of bubbles have been performed in a fixed domain under a constant rate of expansion. A bubble competition is observed: larger bubbles tend to expand more rapidly at the demise of smaller ones. The time scale of competition is shown to depend on a modified Weber number.

physics.flu-dyn↗