In this paper we present a deterministic numerical approximation of the coalescence or Smoluchowski equation. The proposed numerical scheme conserves the first order momentum and deals with non-uniform grids. The generalization to a multidimensional framework is also described. We validate the scheme considering some classical tests both in one and two dimensions and discuss its behavior when gelation occurs. Our numerical results and code are compared with those already existent in literature.
International audienceBubble coalescence is an important process that strongly affects magmatic degassing. Without coalescence, bubbles remain isolated from one another in the melt, severely limiting gas release. Despite this fact, very little has been done to identify coalescence mechanisms from textures of magmatic rocks or to quantify the dynamics of bubble coalescence in melts. In this paper, we present a systematic study of bubble-coalescence mechanisms and dynamics in natural and experimentally produced bubbly rhyolite magma. We have used a combination of natural observations aided by high-resolution X-ray computed tomography, petrological experiments, and physical models to identify different types of bubble-bubble interaction that lead to coalescence on the timescales of magma ascent and eruption. Our observations and calculations suggest that bubbles most efficiently coalesce when inter-bubble melt walls thin by stretching rather than by melt drainage from between converging bubble walls. Orders of magnitude are more rapid than melt drainage, bubble wall stretching produces walls thin enough that inter-bubble pressure gradients may cause the melt wall to dimple, further enhancing coalescence. To put these results into volcanogical context, we have identified magma ascent conditions where each coalescence mechanism should act, and discuss the physical conditions for preserving coalescence structures in natural pumice. The timescales we propose could improve volcanic eruption models, which currently do not account for bubble coalescence. Although we do not address the effect of shear strain on bubble coalescence, the processes discussed here may operate in several different eruption regimes, including vesiculation of lava domes, post-fragmentation frothing of vulcanian bombs, and bubbling of pyroclasts in conduits
We here deal with a model of therapeutic sprays for the upper airways. We aim to model both inhaled and injected sprays. We propose a numerical solver for the kinetic equation which underlies our model, using a particle method. Eventually, we present two numerical tests for simple geometries of the airways. Résumé. Nous proposons dans ce travail une modélisation du comportement d'un brouillard de gouttelettesà but thérapeutique dans les voies respiratoires supérieures. Notre objectif est de mettre en place un modle pouvant représenterà la fois des sprays inhalés et des sprays injectés. Ce modèle est porté par uneéquation cinétique, pour laquelle nous présentons une résolution numérique par méthode particulaire. Enfin, nous donnons deux cas-tests pour des conduits respiratoiresà géométrie simple.
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