Simulation of granular flow and micro-flow

Most flows in mechanical engineering can be described by a set of continuum equations of macroscopic quantities, for example, the Navier-Stokes equations. However there are some flows that cannot properly be described by any continuum descriptions of macroscopic quantities, for example, granular flows and micro-fluid flows.; Granular materials are ensembles of macroscopic particles. The energy dissipation and lack of scale separation put serious limitations on the conventional coarse-graining techniques used for writing a macroscopic theory. We use molecular dynamics simulation to study vertically vibrated granular monolayers and show how the system changes from a gas state to a state that the cluster and gas coexist as the excitation strengths decreases. The dynamics of freely cooling granular gases is also studied. We find that the typical kinetic energy decays algebraically with time and velocity statistics are characterized by a universal Gaussian distribution in the late clustering regime. We also show that particles move coherently as typical local velocity fluctuations are small compared with the typical velocity. Furthermore, locally averaged shear modes dominate over acoustic modes. A heuristical argument suggests that the longtime behavior of freely cooling granular gas can be described by Burgers-like equations. The density fluctuation and cluster size are also investigated.; In micro- and nano-fluid flows, the mean free path of the fluid molecules could be the same order as the typical geometric dimension and the continuum hypothesis breaks down. It is demonstrated that the lattice-Boltzmann method can capture the fundamental behaviors in micro-channel flow, including velocity slip, nonlinear pressure drop along the channel and mass flow rate variation with Knudsen number. The micro-cavity flows is also studied. In most cases the breakdown of the continuum description occurs in small domain regions, such as fluid-solid interfaces and moving contact lines. Hence it is desirable to develop a hybrid method based on continuum and atomistic descriptions using domain decomposition. In the hybrid multiscale method developed by us, the continuum Navier-Stokes equations are used in one flow region and atomistic molecular dynamics in another. The spatial coupling between two descriptions is achieved through constrained dynamics in an overlap region. The proposed hybrid method is used to simulate sudden-start Couette flow and channel flow with nano-scale rough walls, showing quantitative agreement with results from analytical solutions and full molecular dynamics simulations. The micro-cavity flow is simulated and the obvious differences of stress between the hybrid and continuum solutions have been observed since the hybrid method removed the singularity of the continuum equations.