Young Researchers Workshop:
Kinetic and macroscopic models for complex systems

Meshfree particle method for fluctuating hydrodynamic

Anamika Pandey

TU Kaiserslautern

Fluctuating hydrodynamics deals with the thermally induced fluctuations emerge in the fluid. Fluids are essentially noisy due to the thermal fluctuations, which play a key role in the dynamics of fluid. These fluctuations appear due to the molecular nature of the fluid. The fact that the dynamics of fluid at the microscopic scale is sensitive to these fluctuations, is well understood in the literature. However, these fluctuations can also affect the behavior of fluid at larger scale(mesoscopic scale). This work deals with the fluctuations arising in the fluid, at larger scales. In this context, a meshfree formulation of fluctuating hydrodynamics is presented. Fluctuations are modelled at the mesoscopic scale using the Landau-Lifshitz Navier-Stokes (LLNS) equations. The LLNS equations cover a broad range of fluctuating hydrodynamic problems. It is difficult to formulate a numerical approximations providing an accurate and efficient description of the fluctuating hydrodynamics because of the stochastic nature of the underlying fluctuating hydrodynamic equations. A meshfree approximation is even more demanding but the advantages it holds, makes it a preferred choice in many problems such as the problem with time-varying fluid domain. Brownian motion of particles is investigated by direct numerical simulation of the fluctuating hydrodynamic equations. In this framework a bidirectional coupling has been introduced between the fluctuating fluid and the suspended solid object. For the motion of the solid object the required force is extracted from the surrounding fluid particles and no additional force term has been considered in the equations of motion of solid (Newton-Euler equations). Two and three dimensional implementations along with qualitative and quantitative validations are presented. In particular, the Stokes-Einstein relation is reproduced. A meshfree formulation for the fluidstructure interaction subject to thermal fluctuation is a promising approach to deal the study of complex fluid, soft material such as lipid bilayer, polymeric fluids, gel like materials, colloids etc.