Numerical approach to study bubbles and drops evolving through complex geometries by using a level set – Moving mesh – Immersed boundary method

Abstract

The present work proposes a method to study problems of drops and bubbles evolving in complex geometries. First, a conservative level set (CLS) method is enforced to handle the multiphase domain while keeping the mass conservation under control. An Arbitrary Lagrangian-Eulerian (ALE) formulation is proposed to optimize the simulation domain. Thus, a moving mesh (MM) will follow the motion of the bubble, allowing the reduction of the computational domain size and the improvement of the mesh quality. This has a direct impact on the computational resources consumption which is notably reduced. Finally, the use of an Immersed Boundary (IB) method allows to deal with intricate geometries and to reproduce internal boundaries within an ALE framework. The resulting method is capable of dealing with full unstructured meshes. Different problems have been studied to assert the proposed formulation, both involving constricting and non-constricting geometries. In particular, the following problems have been addressed: a 2D gravitydriven bubble interacting with a highly-inclined plane, a 2D gravity-driven Taylor bubble turning into a curved channel, the 3D passage of a drop through a periodically constricted channel, and the impingement of a 3D drop on a flat plate. Good agreement was found for all these cases study, which proves the suitability of the proposed CLS+MM+IB method to study this type of problems.

Numerical Analysis of Viscoelastic Fluid Injection Processes

“…Validations and verifications of the numerical methods used in this work have been reported in [15,16,17,10,18,3,19,20,21]. The Finite-volume (FV) approach is used to discretize the Navier-Stokes and VOF equations on a collocated grid, so all the computed variables are stored at cell centroids.…”

A coupled immersed interface and level set method for simulation of interfacial flows steered by surface tension

“…By the means of  , the singular source term, Γ σκ δ n in Eq. (6) can be expressed as (Chang et al, 1996;Gutiérrez et al, 2018):…”

“…The sharp changes in these physical properties across the interface Γ can pose numerical difficulties (Chang, et al, 1996;Gutiérrez et al, 2018). In order to resolve these issues, the interface is given a fixed thickness ε proportional to mesh spacing h. Firstly, a regularization for δ is introduced using H. Following Peskin (1977), the regularized delta function, ε δ (where ε is typically set to some integral or fractional multiple of h) is defined as…”

“…The time step, t D must adhere to the CFL condition at each iteration due to the presence of convective terms. Therefore, the following restriction is imposed (Gutiérrez et al, 2018):…”

A diffuse domain method for two-phase flows with large density ratio in complex geometries

“…Other methods include boundary integral methods (Biros, Ying & Zorin 2004;Mittal et al 2008), which explicitly incorporate the boundary conditions in the reformulated equations, front-tracking methods (Tryggvason et al 2001;Zolfaghari, Izbassarov & Muradoglu 2017) and arbitrary Eulerian-Lagrangian methods (Hu, Patankar & Zhu 2001;Gilmanov & Sotiropoulos 2005;Anjos et al 2013) that utilize a separate Lagrangian mesh to track the complex boundary and either smear the boundary conditions across several mesh points or explicitly enforce the boundary conditions on the Lagrangian mesh that cuts across the Eulerian mesh using body forces or modified discretizations. Methods along these lines include level-set, ghost-fluid, volume of fluid/level-set and cut-cell methods (Kirkpatrick, Armfield & Kent 2003;Gao et al 2007;Herrmann 2008;de Zélicourt et al 2009;Zhang & Ni 2014;Gutiérrez et al 2018;Cao et al 2019). However, most of these methods require modifications of standard finite element or finite difference software packages.…”