A unified Lagrangian particle approach for the simulation of complex fluids and multi-scale flow phenomena

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In this project, we propose a unified numerical approach for the investigation of complex fluid and multiscale flow problems based on a purely Lagrangian, meshless method, i.e. Smoothed Particle Hydrodynamics (SPH). In order to test the robustness and flexibility of the technique, we will consider two different classes of problems: (1) mesoscopic dynamics of colloids; (2) Lagrangian turbulence. Concerning (1), the central objective will be the development and implementation of an SPH model for the simulation of nanosize structures of arbitrary shapes which are suspended in a continuum medium (Newtonian or non-Newtonian). We propose an investigation of these systems in order to understand their macroscopic rheological behaviour in terms of the micro-mechanical model parameters. With respect to (2), the objective is the modelling of turbulent flows in a fully Lagrangian framework. To this end, we will investigate Lagrangian stochastic models as well as 'sub-particle' scale models based on the recently proposed implicit turbulence modelling approaches, exploiting the specific structure of 'particle methods'. As a result of this project we expect a breakthrough in the purely Lagrangian numerical modelling of turbulence and of viscoelastic materials with inclusions. The unified particle model will be cast into an efficient particle simulation code, where current developments at the host institution are incorporated.