A multiple marker level-set method for simulation of deformable fluid particles

Abstract

A novel multiple marker level-set method is introduced for Direct Numerical Simulation of deformable fluid particles (bubbles and droplets), which is integrated in a finite-volume framework on collocated unstructured grids. Each fluid particle is described by a separate level-set function, thus, different interfaces can be solved in the same control volume, avoiding artificial and potentially unphysical coalescence of fluid particles. Therefore, bubbles or droplets are able to approach each other closely, within the size of one grid cell, and can even collide. The proposed algorithm is developed in the context of the conservative level-set method, whereas, surface tension is modeled by the continuous surface force approach. The pressure-velocity coupling is solved by the fractional-step projection method. For validation of the proposed numerical method, the gravity-driven impact of a droplet on a liquid-liquid interface is studied; then, the binary droplet collision with bouncing outcome is examined, and finally, it is applied on simulation of gravity-driven bubbly flow in a vertical column.

Numerical study of Taylor bubbles rising in a stagnant liquid using a level-set/moving-mesh method

“…The Conservative Level-Set method (CLS) used in the present work was developed by Balcázar et al [21], in the framework of finite-volume discretization and unstructured meshes. This method greatly reduces the problem of mass conservation of the standard Level-Set methods, and it was thoroughly verified in [22,23].…”

A coupled volume-of-fluid/level-set method for simulation of two-phase flows on unstructured meshes

“…Recently, [29] has introduced a conservative level-set method (CLS) where mass conservation problem is greatly reduced, while an hyperbolic tangent function is employed as the level-set function. Moreover, this approach has been generalized to unstructured meshes by [1,2,3], in the framework of finite-volume discretizations.…”

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

“…The CLS formulation dramatically reduces the mass conservation error in comparison with a standard level set method. This technique has been thoroughly verified [30,31].…”

“…The CLS method has been designed for general unstructured meshes [29]. Indeed, the grid can be adapted to any domain, enabling for an efficient mesh distribution in regions where interface resolution has to be maximized [28,29,31,34,35], which is difficult by using structured grids. Furthermore, a TVD fluxlimiter scheme [29] is used to advect the CLS function, avoiding numerical oscillations around discontinuities, whereas the numerical diffusion is minimized.…”