Details

Autor(en) / Beteiligte

• Astuto, Clarissa
• Coco, Armando
• Russo, Giovanni

Titel

A finite-difference ghost-point multigrid method for multi-scale modelling of sorption kinetics of a surfactant past an oscillating bubble

Ist Teil von

• Journal of computational physics, 2023-03, Vol.476, p.111880, Article 111880

Ort / Verlag

Elsevier Inc

Erscheinungsjahr

2023

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We propose a method for the numerical solution of a multiscale model describing sorption kinetics of a surfactant around an oscillating bubble. The evolution of the particles is governed by a convection-diffusion equation for the surfactant concentration c, with suitable boundary condition on the bubble surface, which models the action of the short range attractive-repulsive potential acting on them when they get sufficiently close to the surface [1]. In the domain occupied by the fluid, the particles are transported by the fluid motion generated by the bubble oscillations. The method adopted to solve the equation for c is based on a finite-difference scheme on a uniform Cartesian grid and implemented in 2D and 3D axisymmetric domains. We use a level-set function to define the region occupied by the bubble, while the boundary conditions are discretized by a ghost-point technique to guarantee second order accuracy at the curved boundary. The sparse linear system is finally solved with a geometric multigrid technique designed ad-hoc for this specific problem. Several accuracy tests are provided to prove second order accuracy in space and time. The fluid dynamics generated by the oscillating bubble is governed by the Stokes equation solved with a second order accurate method based on a monolithic approach, where the momentum and continuity equations are solved simultaneously. Since the amplitude of the bubble oscillations are very small, a simplified model is presented where the computational bubble is actually steady and its oscillations are represented purely with time-dependent boundary conditions. A numerical comparison with the moving domain model confirms that this simplification is perfectly reasonable for the class of problems investigated in this paper. •Finite-difference ghost-point methods can be applied to Sorption Kinetics problems.•Time-dependent boundary conditions model the attraction/repulsion mechanism.•The presented 2D and 3D axisymmetric models are second order accurate.•Geometric multigrid efficiency is not affected by curved boundary and moving bubble.•Small oscillations can be accurately captured by computational steady bubbles.