Resolving the fine-scale structure in turbulent Rayleigh-Benard convection

We present high-resolution direct numerical simulation studies of turbulent Rayleigh-Benard convection in a closed cylindrical cell with an aspect ratio of one. The focus of our analysis is on the finest scales of convective turbulence, in particular the statistics of the kinetic energy and thermal dissipation rates in the bulk and the whole cell. The fluctuations of the energy dissipation field can directly be translated into a fluctuating local dissipation scale which is found to develop ever finer fluctuations with increasing Rayleigh number. The range of these scales as well as the probability of high-amplitude dissipation events decreases with increasing Prandtl number. In addition, we examine the joint statistics of the two dissipation fields and the consequences of high-amplitude events. We also have investigated the convergence properties of our spectral element method and have found that both dissipation fields are very sensitive to insufficient resolution. We demonstrate that global transport properties, such as the Nusselt number, and the energy balances are partly insensitive to insufficient resolution and yield correct results even when the dissipation fields are under-resolved. Our present numerical framework is also compared with high-resolution simulations which use a finite difference method. For most of the compared quantities the agreement is found to be satisfactory.Comment: 33 pages, 24 figure

Reactive Rayleigh-Taylor Turbulence

The Rayleigh-Taylor (RT) instability develops and leads to turbulence when a heavy fluid falls under the action of gravity through a light one. We consider this phenomenon accompanied by a reactive transformation between the fluids, and study with Direct Numerical Simulations (DNS) how the reaction (flame) affects the turbulent mixing in the Boussinesq approximation. We discuss "slow" reactions where the characteristic reaction time exceeds the temporal scale of the RT instability. In the early turbulent stage, effects of the flame are distributed over a maturing mixing zone, whose development is weakly influenced by the reaction. At later times, the fully mixed zone transforms into a conglomerate of pure-fluid patches of sizes proportional to the mixing zone width. In this "stirred flame'' regime, temperature fluctuations are consumed by reactions in the regions separating the pure-fluid patches. This DNS-based qualitative description is followed by a phenomenology suggesting that thin turbulent flame is of a single-fractal character, and thus distribution of the temperature field is strongly intermittent.Comment: 14 pages, 4 figure

On the miscible Rayleigh-Taylor instability: two and three dimensions

We investigate the miscible Rayleigh-Taylor (RT) instability in both 2 and 3 dimensions using direct numerical simulations, where the working fluid is assumed incompressible under the Boussinesq approximation. We first consider the case of randomly perturbed interfaces. With a variety of diagnostics, we develop a physical picture for the detailed temporal development of the mixed layer: We identify three distinct evolutionary phases in the development of the mixed layer, which can be related to detailed variations in the growth of the mixing zone. Our analysis provides an explanation for the observed differences between two and three-dimensional RT instability; the analysis also leads us to concentrate on the RT models which (1) work equally well for both laminar and turbulent flows, and (2) do not depend on turbulent scaling within the mixing layer between fluids. These candidate RT models are based on point sources within bubbles (or plumes) and interaction with each other (or the background flow). With this motivation, we examine the evolution of single plumes, and relate our numerical results (of single plumes) to a simple analytical model for plume evolution.Comment: 31 pages, 27 figures, to appear in November issue of JFM, 2001. For better figures: http://astro.uchicago.edu/~young/ps/jfmtry08.ps.

Investigation of the Global Instability of the Rotating-disk Boundary Layer

The development of the flow over a rotating disk is investigated by direct numerical simulations using both the linearized and fully nonlinear incompressible Navier–Stokes equations. These simulations allow investigation of the transition to turbulence of the realistic spatially-developing boundary layer. The current research aims to elucidate further the global linear stability properties of the flow, and relate these to local analysis and discussions in literature. An investigation of the nonlinear upstream (inward) influence is conducted by simulating a small azimuthal section of the disk (1/68). The simulations are initially perturbed by an impulse disturbance where, after the initial transient behaviour, both the linear and nonlinear simulations show a temporally growing upstream mode. This upstream global mode originates in the linear case close to the end of the domain, excited by an absolute instability at this downstream position. In the nonlinear case, it instead originates where the linear region ends and nonlinear harmonics enter the flow field, also where an absolute instability can be found. This upstream global mode can be shown to match a theoretical mode from local linear theory involved in the absolute instability at either the end of the domain (linear case) or where nonlinear harmonics enter the field (nonlinear case). The linear simulation grows continuously in time whereas the nonlinear simulation saturates and the transition to turbulence moves slowly upstream towards smaller radial positions asymptotically approaching a global upstream mode with zero temporal growth rate, which is estimated at a nondimensional radius of 582.Swedish Research Counci

Dynamic Load Balancing for Compressible Multiphase Turbulence

CMT-nek is a new scientific application for performing high fidelity predictive simulations of particle laden explosively dispersed turbulent flows. CMT-nek involves detailed simulations, is compute intensive and is targeted to be deployed on exascale platforms. The moving particles are the main source of load imbalance as the application is executed on parallel processors. In a demonstration problem, all the particles are initially in a closed container until a detonation occurs and the particles move apart. If all processors get an equal share of the fluid domain, then only some of the processors get sections of the domain that are initially laden with particles, leading to disparate load on the processors. In order to eliminate load imbalance in different processors and to speedup the makespan, we present different load balancing algorithms for CMT-nek on large scale multi-core platforms consisting of hundred of thousands of cores. The detailed process of the load balancing algorithms are presented. The performance of the different load balancing algorithms are compared and the associated overheads are analyzed. Evaluations on the application with and without load balancing are conducted and these show that with load balancing, simulation time becomes faster by a factor of up to $9.97$.Comment: This paper has been accepted by ACM International Conference on Supercomputing (ICS) 201

Multirate Timestepping for the Incompressible Navier-Stokes Equations in Overlapping Grids

We develop a multirate timestepper for semi-implicit solutions of the unsteady incompressible Navier-Stokes equations (INSE) based on a recently-developed multidomain spectral element method (SEM). For {\em incompressible} flows, multirate timestepping (MTS) is particularly challenging because of the tight coupling implied by the incompressibility constraint, which manifests as an elliptic subproblem for the pressure at each timestep. The novelty of our approach stems from the development of a stable overlapping Schwarz method applied directly to the Navier-Stokes equations, rather than to the convective, viscous, and pressure substeps that are at the heart of most INSE solvers. Our MTS approach is based on a predictor-corrector (PC) strategy that preserves the temporal convergence of the underlying semi-implicit timestepper. We present numerical results demonstrating that this approach scales to an arbitrary number of overlapping grids, accurately models complex turbulent flow phenomenon, and improves computational efficiency in comparison to singlerate timestepping-based calculations.Comment: 40 pages, 13 figure