High fidelity anisotropic adaptive variational multiscale method for multiphase flows with surface tension

A VOSET method combined with IDEAL algorithm for 3D two-phase flows with large density and viscosity ratio

Comparison of surface tension generation methods in smoothed particle hydrodynamics for dynamic systems

One of the fundamental problems in simulating the motion of sharp interfaces between immiscible fluids is a description of the transition that occurs when the interfaces merge and reconnect. It is well known that classical methods involving sharp interfaces fail to describe this type of phenomena. Following some previous work in this area, we suggest a physically motivated regularization of the Euler equations which allows topological transitions to occur smoothly. In this model, the sharp interface is replaced by a narrow transition layer across which the fluids may mix. The model describes a flow of a binary mixture, and the internal structure of the interface is determined by both diffusion and motion. An advantage of our regularization is that it automatically yields a continuous description of surface tension, which can play an important role in topological transitions. An additional scalar field is introduced to describe the concentration of one of the fluid components and the resulting system of equations couples the Euler (or Navier–Stokes) and the Cahn–Hilliard equations. The model takes into account weak non–locality (dispersion) associated with an internal length scale and localized dissipation due to mixing. The non–locality introduces a dimensional surface energy; dissipation is added to handle the loss of regularity of solutions to the sharp interface equations and to provide a mechanism for topological changes. In particular, we study a non–trivial limit when both components are incompressible, the pressure is kinematic but the velocity field is non–solenoidal (quasi–incompressibility). To demonstrate the effects of quasi–incompressibility, we analyse the linear stage of spinodal decomposition in one dimension. We show that when the densities of the fluids are not perfectly matched, the evolution of the concentration field causes fluid motion even if the fluids are inviscid. In the limit of infinitely thin and well–separated interfacial layers, an appropriately scaled quasi–incompressible Euler–Cahn–Hilliard system converges to the classical sharp interface model. In order to investigate the behaviour of the model outside the range of parameters where the sharp interface approximation is sufficient, we consider a simple example of a change of topology and show that the model permits the transition to occur without an associated singularity.

A simplified method is proposed to implement a wetting boundary condition on curved surfaces within the conservative phase-field lattice-Boltzmann (LB) simulation framework. It combines the idea of Huang et al. [“An alternative method to implement contact angle boundary condition and its application in hybrid lattice-Boltzmann finite-difference simulations of two-phase flows with immersed surfaces,” Eur. Phys. J. E 41, 17 (2018)] to find the order parameter on the other side of the wall with the conservative Allen–Cahn equation (CACE) for interface evolution solved by the LB equations. It inherits the advantage of the original method using the Cahn–Hilliard equation to avoid complicated interpolations under different geometries. By using the CACE, the boundary condition for the chemical potential is circumvented (making it more simplified), and the overshooting of the order parameter is also greatly suppressed, enabling it to simulate two-phase flows with solid objects of various shapes and wettabilities at large density and viscosity ratios. Several two-dimensional, axisymmetric, and three-dimensional problems, including some previously studied by experiments, were simulated and the capability of the proposed method is demonstrated through its good agreement with theoretical predictions and/or experimental observations.

We consider adaptive discontinuous Galerkin (DG) methods for solving reactive transport problems in porous media. To guide anisotropic and dynamic mesh adaptation, a posteriori error estimators based on solving local problems are established. These error estimators are efficient to compute and effective to capture local phenomena, and they apply to all the four primal DG schemes, namely, symmetric interior penalty Galerkin, nonsymmetric interior penalty Galerkin, incomplete interior penalty Galerkin, and the Oden–Babuska-Baumann version of DG. Numerical results are provided to illustrate the effectiveness of the proposed error estimators.

A multiphase MPS method for bubbly flows with complex interfaces

The aim of this paper is to utilize a numeri- cal model to compute bubble motion in quiescent Newto- nian and viscoelastic liquids. For our numerical method, we use a coupled level set and volume-of-fluid method with a second order treatment for the jump conditions related to surface tension. We investigate axisymmetric gas-liquid systems with large density and viscosity ratios as well as buoyancy-driven flows with complex changes in topology. We present comparisons to previous compu- tational results as well as experimental results. keyword: Level set, Volume-of-fluid, Viscoelastic, Projection method, Adaptive mesh refinement

A multiphase lattice Boltzmann model is constructed to numerically solve the one-fluid flow equations for immiscible fluids. The method features one solver for the macroscopic pressure and momentum and another for a scalar field that captures and sharpens the interface. The surface tension is set a priori and independently of other parameters. The interface capillary tensor is embedded within the moments of the lattice Boltzmann equation so that its divergence is captured locally. The algorithm is simple and can compute flows with large density and viscosity ratios while maintaining distributed but narrow interfaces. The model is validated against analytical solutions and benchmark simulations.

Thermodynamic consistency is a key factor in heat and mass transfer simulation. A modified lattice Boltzmann pseudopotential model with the ability to simulate multiphase and multicomponent flow with a large density and viscosity ratio is proposed. Relative to a model using the exact difference method, a better thermodynamic consistency is obtained through introducing an improved external force term, a multi-relaxation-time collision operator, and a scaling coefficient k of the equation of state. The coefficient of scale k = 0.1 is preferred due to its better thermodynamic consistency, lower spurious current and a smaller surface tension. The inter-particle interaction strength has little influence over the thermodynamic consistency due to its limited contributions to the surface tension. With the model, the bubble dissolution under pressure is investigated and Henry’s law is validated.

Diffuse interface modeling of three-phase contact line dynamics on curved boundaries: A lattice Boltzmann model for large density and viscosity ratios

Adaptive variational multiscale methods for incompressible flow based on two local Gauss integrations

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.

Two-fluid immiscible displacement flow through a zone of different wettability in a porous medium has been studied. A deterministic model based on a microscopic approach has been used to determine the flow pattern of the invading fluid, The porous medium is represented by a two-dimensional square network of interconnected channels. Computer simulations for three distinct wettability cases and for four different values of the capillary number show that the effects of heterogeneity of the wettability on the behaviour of the invading fluid are very strong when capillary forces are significant and even stronger when there is a wettability contrast from an oil-wet to water-wet zone in the porous medium. Introduction An understanding of how heterogeneities m wettability affect displacement flow in porous media is fundamental to the study of water/oil displacement processes in underground petroleum reservoirs. As noted by Morro(1), the reservoir wettability is not a simply defined property and the classification of reservoirs as being either oil-wet or water-wet constitutes a great oversimplification (measurements show that reservoir wettability can cover a broad spectrum of wetting conditions that range from water-wet to oil-wet). As further noted by Morrow(1), there has been a notable revival during the last decade ill the mathematical analysis of pore networks for modelling displacement processes in porous media, and the choice of the assumptions and rules to account for wettability effects in network models is a problem that has only recently begun to receive the attention that it deserves. The present study investigates two-fluid displacement flow through a porous medium containing a zone of different wettability. The porous medium is represented by a two-dimensional square network of interconnected channels. The wettability is characterized by cos θ where θ is the contact angle between the solid surface and the fluid interface measured through the displaced phase. Thus, for cos θ = 1, we have drainage displacement of a strongly wetting fluid (W) by a non-wetting fluid (NW). For cos θ = -1, we have imbibition displacement of a non-wetting fluid by a strongly wetting fluid. Finally, for cos θ = 0. we have neutralwettability. In the present work three cases are examined (Figure 1), namely (a) drainage displacement in a macroscopically homogeneous porous medium, (b) drainage displacement in the presence of a central zone of neutral wettability, and (c) drainage displacement in the presence of a central zone where imbibition takes place (cos θ = -1). Computer simulations have been performed in order to examine these three cases in terms of the interplay between viscous and capillary forces as expressed by the capillary number. NCi = V μi/ γcos θ, defined at injection conditions where V is the injection velocity of the invading fluid, i the viscosity of the invading fluid and γ the interfacial tension. The viscosity ratio, M = μi/ μd, is defined as the ratio of the viscosity of the invading fluid, μi, to that of the displaced fluid, μd. The viscosity ratio is maintained constant at M = 0.1 for the entire series of simulations undertaken in the present work.

Effects of viscosification, ultra-low interfacial tension, and emulsification on heavy oil recovery by combination flooding

Consistent mass and momentum transport for simulating incompressible interfacial flows with large density ratios using the level set method