Criterion of drop fragmentation at a collision with a solid target (numerical simulation and experiment)

This paper is devoted to the study of the deformation and fragmentation of liquid droplets when they collide with masks and filters used for protection against infected droplets. In this paper, the local collision of a drop with a mask or filter is modeled numerically and experimentally by the example of the drop impact on a small obstacle. Studies allow tracing the fragmentation of oral and bronchial fluids and their transformation into the number of tiny droplets that spread infection in the air.

The influence of an impedance obstacle on the acoustic field inside a rectangular room

The problem of sound propagation inside a rigid-walled room containing a rectangular obstacle was solved by dividing an acoustic field into subregions and using the continuity conditions. Acoustic waves were generated by a point source. The formulas valid for an impedance obstacle extending from a room floor to its ceiling were obtained. The considered obstacle can modeled such elements as a ventilation shaft, furniture or construction pillar. The solution was expressed in the form of convergent series. To obtain accurate results, the error resulting from the use of truncated series was controlled. Additionally, to check a correctness of the proposed solution and its computer implementation, the results obtained for a negligibly small obstacle were compared with those given by the empty room model. An excellent agreement was achieved which proves a high accuracy of the used methodology. The numerical analysis shown that the calculation time of acoustic pressure in a part of an empty room can be significantly reduced by using the obtained solution. An optimal source location for noise reduction was found. The distribution of acoustic field was illustrated and some conclusions were formulated. The changes in acoustic field due to the obstacle presence were predicted and discussed.

The Elastic Flow with Obstacles: Small Obstacle Results

We consider a parabolic obstacle problem for Euler’s elastic energy of graphs with fixed ends. We show global existence, well-posedness and subconvergence provided that the obstacle and the initial datum are suitably ‘small’. For symmetric cone obstacles we can improve the subconvergence to convergence. Qualitative aspects such as energy dissipation, coincidence with the obstacle and time regularity are also examined.

Topological asymptotic formula for the 3D non-stationary Stokes problem and application

International audience This paper is concerned with a topological asymptotic expansion for a parabolic operator. We consider the three dimensional non-stationary Stokes system as a model problem and we derive a sensitivity analysis with respect to the creation of a small Dirich-let geometric perturbation. The established asymptotic expansion valid for a large class of shape functions. The proposed analysis is based on a preliminary estimate describing the velocity field perturbation caused by the presence of a small obstacle in the fluid flow domain. The obtained theoretical results are used to built a fast and accurate detection algorithm. Some numerical examples issued from a lake oxygenation problem show the efficiency of the proposed approach. Ce papier porte sur l'analyse de sensibilité topologique pour un opérateur parabolique. On considère le problème de Stokes instationnaire comme un exemple de modèle et on donne une étude de sensibilité décrivant le comportement asymptotique de l'opérateur relativement à une petite perturbation géométrique du domaine. L'analyse présentée est basée sur une estimation du champ de vitesse calculée dans le domaine perturbé. Les résultats de cette étude ont servi de base pour développer un algorithme d'identification géométrique. Pour la validation de notre approche, on donne une étude numérique pour un problème d'optimisation d'emplacement des injecteurs dans un lac eutrophe. Des exemples numériques montrent l'efficacité de la méthode proposée

Kohn-Vogelius formulation and high-order topological asymptotic formula for identifying small obstacles in a fluid medium

This paper concerns the identification of a small obstacle immersed in a Stokes flow from boundary measurements. The proposed approach is based on the Kohn-Vogelius formulation and the topological sensitivity analysis method. We derive a high order asymptotic formula describing the variation of a Kohn-Vogelius type functional with respect to the insertion of a small obstacle inside the fluid flow domain. The obtained asymptotic formula will serve as very useful tools for developing accurate and robust numerical reconstruction algorithms.