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Theses

Micro/macro coupling for the simulation of shock and detonation waves

Abstract : This thesis studies mesoscopic models adapted to the simulation of shock and detonation waves in fluids. These phenomena require systems sufficiently large to observe the complex processes occurring in this context. The aim is thus to increase the accessible time and length scales of microscopic methods, accurate but expensive, while preserving their essential properties. To this end, the multiscale coupling of methods at different resolutions allows to finely describe a specific region, limiting the computational cost. In particular, we study Smoothed Dissipative Particle Dynamics (SDPD) which couples a particle discretization of the Navier-Stokes equations and thermal fluctuations that scale consistently with the resolution. The SDPD equations are reformulated in terms of internal energies, which increases the structural similarity with Dissipative Particle Dynamics with Energy conservation (DPDE). We adapt numerical schemes for DPDE to the context of SDPD in order to ensure energy conservation and stability. We study the statistical properties of SDPD and determine estimators for temperature and pressure. The size consistency in SDPD is established for equilibrium and shock waves, which leads us to propose a multiscale coupling of SDPD at different resolutions. Finally, its physical relevance is illustrated by simulating micro-jetting and detonation waves.
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Submitted on : Saturday, December 2, 2017 - 4:58:38 PM
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Gérôme Faure. Micro/macro coupling for the simulation of shock and detonation waves. Mathematics [math]. Université Paris-Est, 2017. English. ⟨tel-01652989⟩

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