02 Décembre – Thesis defense - Félix Henri

14 h Amphi G - ENSEIRB-MATMECA (Talence)

Improvements in Level Set methods for raindrop impact.

The dynamics of two-phase flows mixing different spatial scales, large interface deformations and topology changes are complex and challenging to simulate numerically. The use of robust and high-order methods is essential, particularly when surface tension forces are considered. A key point is the method for following the interface between the two fluids. For this purpose, the Level Set approach is an appropriate choice. Indeed, its implicit representation of the interface provides an accurate and simple way of calculating the geometric quantities related to it and furthermore, changes in topology are naturally captured. Nevertheless, this method is not without flaws, since the conservation of volumes is not perfect and a so-called reinitialization step is necessary.
In this work, after presenting the Level Set method, we introduce the notion of kinks, points of the level set function where derivative or interpolation calculations will be subject to strong errors. An algorithm is proposed to detect them. Then, a new approach for the reinitialization step is presented, the RCP method (Reinitialization with Closest Point method) which relies on a gradient descent algorithm for computing the closest points to the interface and on the kink detection algorithm. Additionally, a hybrid method, named HWH5, coupling a WENO5,3 scheme and a HOUC5 scheme, is proposed for the advection equation. In order to evaluate the performance of the proposed methods, they are tested on various cases from the literature. We demonstrate that the RCP method presents better or at least equivalent results to the classical approach based on the solution of a Hamilton-Jacobi equation and hence represents a compelling alternative. Moreover, we also show that HWH5 provides a scheme that is as accurate and robust as a WENO5,3 scheme with a computational cost reduced by a factor up to 2. Finally, simulations of droplet impacts on a liquid surface are presented. The objective is to demonstrate that the numerical methods developed are suitable for capturing complex flows where surface tension forces are predominant and where some delicate phenomena emerge, such as the formation of an extremely fine ascending central jet that breaks up into multiple droplets.

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