We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two identical fluids. The steady-state diffusive flux in a finite system subject to a concentration gradient is enhanced because of long-range correlations between concentration fluctuations and fluctuations of the velocity parallel to the concentration gradient. The enhancement of the diffusive transport depends on the system size L and grows as ln(L/L0) in quasi-two-dimensional systems, while in three dimensions it grows as L0 − 1 − L − 1, where L0 is a reference length. The predictions of a simple fluctuating hydrodynamics theory, closely related to second-order mode–mode coupling analysis, are compared to results from particle simulations and a finite-volume solver and excellent agreement is observed. We elucidate the direct connection to the long-time tail of the velocity autocorrelation function in finite systems, as well as finite-size corrections employed in molecular dynamics calculations. Our results conclusively demonstrate that the nonlinear advective terms need to be retained in the equations of fluctuating hydrodynamics when modeling transport in small-scale finite systems.
In this paper we present a second-order accurate adaptive algorithm for solving multiphase, incompressible flows in porous media. We assume a multiphase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting the total velocity, defined to be the sum of the phase velocities, is divergence-free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids areadvanced multiple steps to reach the same time as the coarse grids and the data atdifferent levels are then synchronized. The single grid algorithm is described briefly,but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm's accuracy and convergencemore » properties and to illustrate the behavior of the method.« less
Lack of resolution is a common problem hampering the use of large eddy simulation models for investigating boundary layer dynamics. Entrainment into the tops of marine stratus is characteristic of this problem. The use of parallel computing as a technique for resolving both boundary layer motions and the entrainment region enables the investigation of the interaction between the moist thermodynamics and turbulence in the entrainment region at very small length scales (dx = 8 m, dz = 4 m). This interaction results in heterogeneity at small scales which is important for correctly diagnosing the details of entrainment. This study presents several numerical experiments at high resolution using a generalization of a 1995 GCSS (GEWEX Cloud System Studies) model intercomparison. Subtle details of the numerical algorithm are found to cause larger differences in entrainment than choice of subgrid model. A kinetic energy budget shows that even for very high resolution, numerical dissipation is usually larger than that produced by the subgrid model. However, the structure of eddies at the inversion is determined mainly by resolution with very little dependence on numerical representation. Inversion properties are converging as resolution approaches an undulation scale. Most of the mixing is confined within 100 meters of the inversion with entraining motions having an aspect ratio of 6 to 1.
Axisymmetric numerical simulations continue to provide new insight into how the structure, dynamics, and maximum windspeeds of tornadoes, and other convectively-maintained vortices, are influenced by the surrounding environment. This work is continued with a new numerical model of axisymmetric incompresible flow that incorporates adaptive mesh refinement. The model dynamically increases or decreases the resolution in regions of interest as determined by a specified refinement criterion. Here, the criterion used is based on the cell Reynolds number, so that the flow is guaranteed to be laminar on the scale of the local grid spacing. The power of adaptive mesh refinement is used to investigate the effects of the size of the domain, the location and geometry of the convective forcing, and the effective Reynolds number (based on the choice of the eddy viscosity ν) on the behavior of the vortex. In particular, the claim that the vortex Reynolds number Γ/ν, which the ratio of the far-field circulation to the eddy viscosity, is the most important parameter for determining vortex structure and behavior is found to be valid over a wide variety of domain and forcing geometries. Furthermore, it is found that the vertical scale of the convective forcing only affects the vortex inasmuch as this vertical scale contributes to the total strength of the convective forcing. The horizontal scale of the convective forcing, however, is found to be the fundamental length scale in the problem, in that it can determine both the circulation of the fluid that is drawn into the vortex core, and also influences the depth of the swirling boundary layer. Higher mean windspeeds are sustained as the eddy viscosity is decreased; however, it is observed that that the highest windspeeds are found in the high-swirl, two-celled vortex regime rather than in the low-swirl, one-celled regime, which is opposite to
Artifact Description See https://zenodo.org/record/7790160 (and update). Milestone data for year 7, milestone 2 (WBS 2.2.2.6, Milestone ECP-ADSE06.FY23.2).
This dataset includes the inputs, outputs, job submission scripts, and data analysis scripts used to prepare the WarpX milestone report for "Assessment of dynamic load-balancing strategies on available exascale systems." The code versions of WarpX, AMReX, and PICSAR used are stored in the outputs file for each run.
We present three-dimensional, time-dependent simulations of a full-size laboratory-scale rod-stabilized premixed turbulent V-flame. The computations use an adaptive projection method based on a low Mach number formulation that incorporates detailed chemical kinetics and transport. The simulations are performed without introducing models for turbulence or turbulence chemistry interaction. We outline the numerical procedure and experimental setup, and compare computed results to mean flame location and surface wrinkling statistics gathered from experiment.
We develop a one-dimensional theoretical model for thermals burning in Type Ia supernovae based on the entrainment assumption of Morton, Taylor, and Turner. Extensions of the standard model are required to account for the burning and for the expansion of the thermal due to changes in the background stratification found in the full star. The model is compared with high-resolution three-dimensional numerical simulations, both in a uniform environment and a full-star setting. The simulations in a uniform environment present compelling agreement with the predicted power laws and provide model constants for the full-star model, which then provides excellent agreement with the full-star simulation. The importance of the different components in the model is compared, and are all shown to be relevant. An examination of the effect of initial conditions was then conducted using the one-dimensional model, which would have been infeasible in three dimensions. More mass was burned when the ignition kernel was larger and closer to the center of the star. The turbulent flame speed was found to be important during the early-time evolution of the thermal, but played a diminished role at later times when the evolution is dominated by the large-scale hydrodynamics responsible for entrainment. However, a higher flame speed effectively gave a larger initial ignition kernel and so resulted in more mass burned. This suggests that future studies should focus on the early-time behavior of these thermals (in particular, the transition to turbulence), and that the choice of turbulent flame speed does not play a significant role in the dynamics once the thermal has become established.
