Session PR: General Fluid Mechanics: Numerical Simulations

Chaotic Advection with Inertia in a 2D Cavity Flow

The mechanisms underlying chaotic advection and mixing in inertial flow above the Stokes flow regime are incompletely understood. We performed numerical simulations of chaotic advection and mixing for time-periodic inertial flow in a two-dimensional rectangular cavity driven by alternating motion of the upper and lower walls. The effects of inertia were analyzed in terms of the flow topology and tracer dynamics. The Poincar\'{e} map evolves as the Reynolds number increases. Periodic points shift in position from their original locations in Stokes flow, and the Poincar\'{e} sections transition from those characteristic of Stokes flow to a different characteristic pattern at higher Reynolds numbers. Tracer motion exhibits increasing degrees of disorder with increasing Reynolds number and decreasing forcing frequency resulting in increased chaotic mixing. The forcing frequency has a much greater impact on chaotic advection and mixing than inertial effects.   

Realistic Simulations of the Turbulent Plasma Dynamics on the Sun

The objective of this research is to model the turbulent dynamics of the upper convective boundary layer of the Sun and investigate how magnetic field affects the structure and dynamics of solar convection and the sources that drive the waves in the Sun. We use a 3D, compressible, non-linear radiative magnetohydrodynamics code developed by Alan Wray for simulating the upper solar convection zone and the lower atmosphere. We have carried out the numerical simulations using a hyperviscosity approach and various physical Large-Eddy Simulation (LES) models (Smagorinsky and dynamic models) to investigate how the differences in turbulence modeling affect the damping and excitation of the oscillations and their spectral properties and to compare with observations from the SOHO and Hinode space missions. We find that the dynamic turbulence model provides the best agreement with the observations. We have studied the effects of magnetic field on the spatial-temporal spectrum of the turbulent convection, and found that these simulations can explain the observed changes of the granular dynamics and the enhanced emission of high-frequency waves in magnetic regions (effect of ``acoustic halo'').   

Direct Numerical Simulation of the turbulent flow over an urban canopy made of cubical obstacles

Computations of flow over staggered arrays of cubes with various plan area density are presented and discussed. A DNS technique, using an immersed boundary method for the obstacles, was employed. It is shown that the surface drag is predominantly form drag, which has a maximum for an area coverage around 15{\%}. As the effective roughness of the surface increases, so does the ratio of the spatially averaged vertical and axial normal turbulence stresses at the obstacle height, so a major effect of roughness is to change the structure of the turbulence field, thus altering the way that pollutants emitted within the canopy are transported. Time history of the total drag shows large scale oscillations. This should be related to large-scale pair of axially-orientated vortex rolls which are not stable, but ``come and go'' roughly periodically in time. These vortex structures appear to be much weaker when the total drag has its lowest magnitude. Such rolls are perhaps not unexpected. They have been found in boundary layers developing over similar surfaces but in that case appear to be essentially steady.   

A front tracking technique for direct numerical simulations of multiphase flows in complex geometries

Experimental studies have been the main thrust of microfluidic research so far; however, numerical simulations are gradually gaining acceptance as their importance is being more and more recognized by researchers in the field. Accurately capturing the liquid/liquid or liquid/gas interface is only part of the challenge in simulating fluid flow in lab-on-a-chip; the complex solid boundaries must also be accurately represented. Handling complex boundaries has been one of the challenges of CFD from the very beginning and one can identify roughly three stages. Crude representation of curved boundaries on a fixed grid by stair-stepping, body-fitted structured grids, and body-fitted unstructured grids. Current commercial codes almost exclusively use some variants of the last approach. However, while very common, unstructured grids generally lead to inefficient and inaccurate codes. Here, we present a front tracking technique to simulate the motion of drops and bubbles through complex geometries using regular structured meshes, where solid boundaries are represented as immersed boundaries and fluid boundaries are explicitly tracked. The methodology is validated and the code is used to study the dynamics of pressure-driven bubbles in a complex network of channels.   

Study on the preconditioning method of a finite element combined formulation for fluid-structure interaction

Preconditioners for a two-dimensional combined finite element formulation were devised and tested for fluid-structure interaction (FSI) problems. A fluid-structure interaction code simulating the interaction of circular bodies with an unsteady flow is based on a P2P1 finite element method using combined formulation. Extending the AILU preconditioners proposed by Nam et al.[2002] for P2P1 finite element formulation, four preconditioners were proposed for combined finite element formulation. Numerical simulations were performed for some two-dimensional FSI problems. It has been shown that two preconditioners among them perform well with respect to computational memory and convergence for a bench-mark problem.   

Vorticity dynamics in turbulence growth

The statistical and structural properties of fully developed isotropic turbulence can be reproduced at high $R_\lambda$ by numerical simulation with random forcing at large scales. A $k^{-5/3}$ energy spectrum range is observed. To understand why this range is formed inviscid and viscous time developing numerical simulations are performed starting with a certain number of Lamb dipoles. Inviscid simulations lead to a very strong vorticity amplification, which close to the eventual finite time singularity produces a $k^{-3}$ range. The viscous simulations, depending on the viscosity, show an enstrophy production differing from the inviscid simulations. the enstrophy dissipation becomes of the same order of the enstrophy production, which does not blows-up and reaches a maximum. At this point the $k^{-5/3}$ range forms. The analysis in the strain-rate tensor principal axes shows that the enstrophy production is correlated with the intermediate $\widetilde{S}_2$ accounting for sheet-like structures.