A comparative analysis of parallel processing and super-individual methods for improving the computational performance of a large individual-based model

Individual-based modelling approaches are being used to simulate larger complex spatial systems in ecology and in other fields of research. Several novel model development issues now face researchers: in particular how to simulate large numbers of individuals with high levels of complexity, given finite computing resources. A case study of a spatially-explicit simulation of aphid population dynamics was used to assess two strategies for coping with a large number of individuals: the use of ‘super-individuals’ and parallel computing. Parallelisation of the model maintained the model structure and thus the simulation results were comparable to the original model. However, the super-individual implementation of the model caused significant changes to the model dynamics, both spatially and temporally. When super-individuals represented more than around 10 individuals it became evident that aggregate statistics generated from a super-individual model can hide more detailed deviations from an individual-level model. Improvements in memory use and model speed were perceived with both approaches. For the parallel approach, significant speed-up was only achieved when more than five processors were used and memory availability was only increased once five or more processors were used. The super-individual approach has potential to improve model speed and memory use dramatically, however this paper cautions the use of this approach for a density-dependent spatially-explicit model, unless individual variability is better taken into account

Large-eddy simulation of three-dimensional dunes in a steady, unidirectional flow. Part 2. Flow structures

We performed large-eddy simulations of the flow over a series of three-dimensional (3D) dunes at laboratory scale. The bedform three-dimensionality was imposed by shifting a standard two-dimensional (2D) dune shape in the streamwise direction according to a sine wave. The turbulence statistics were discussed in Part 1 of this article (Omidyeganeh & Piomelli, J. Fluid Mech., vol. 721, 2013, pp. 454–483). Coherent flow structures and their statistics are discussed concentrating on two cases with the same crestline amplitudes and wavelengths but different crestline alignments: in-phase and staggered. The present paper shows that the induced large-scale mean streamwise vortices are the primary factor that alters the features of the instantaneous flow structures. Wall turbulence is insensitive to the crestline alignment; alternating high- and low-speed streaks appear in the internal boundary layer developing on the stoss side, whereas over the node plane (the plane normal to the spanwise direction at the node of the crestline), they are inclined towards the lobe plane (the plane normal to the spanwise direction at the most downstream point of the crestline) due to the mean spanwise pressure gradient. Spanwise vortices (rollers) generated by Kelvin–Helmholtz instability in the separated shear layer appear regularly over the lobe with much larger length scale than those over the saddle (the plane normal to the spanwise direction at the most upstream point of the crestline). Rollers over the lobe may extend to the saddle plane and affect the reattachment features; their shedding is more frequent than in 2D geometries. Vortices shed from the separated shear layer in the lobe plane undergo a three-dimensional instability while being advected downstream, and rise toward the free surface. They develop into a horseshoe shape (similar to the 2D case) and affect the whole channel depth, whereas those generated near the saddle are advected downstream and toward the bed. When the tip of such a horseshoe reaches the free surface, the ejection of flow at the surface causes ‘boils’ (upwelling events on the surface). Strong boil events are observed on the surface of the lobe planes of 3D dunes more frequently than in the saddle planes. They also appear more frequently than in the corresponding 2D geometry. The crestline alignment of the dune alters the dynamics of the flow structures, in that they appear in the lobe plane and are advected towards the saddle plane of the next dune, where they are dissipated. Boil events occur at a higher frequency in the staggered alignment, but with less intensity than in the in-phase alignment

Large-eddy simulation of three-dimensional dunes in a steady, unidirectional flow. Part 1. Turbulence statistics

We performed large-eddy simulations of flow over a series of three-dimensional dunes at laboratory scale (Reynolds number based on the average channel depth and streamwise velocity was 18 900) using the Lagrangian dynamic eddy-viscosity subgrid-scale model. The bedform three-dimensionality was imposed by shifting a standard two-dimensional dune shape in the streamwise direction according to a sine wave. The statistics of the flow are discussed in 10 cases with in-phase and staggered crestlines, different deformation amplitudes and wavelengths. The results are validated qualitatively against experiments. The three-dimensional separation of flow at the crestline alters the distribution of wall pressure, which in turn may cause secondary flow across the stream, which directs low-momentum fluid, near the bed, toward the lobe (the most downstream point on the crestline) and high-momentum fluid, near the top surface, toward the saddle (the most upstream point on the crestline). The mean flow is characterized by a pair of counter-rotating streamwise vortices, with core radius of the order of the flow depth. However, for wavelengths smaller than the flow depth, the secondary flow exists only near the bed and the mean flow away from the bed resembles the two-dimensional case. Staggering the crestlines alters the secondary motion; the fastest flow occurs between the lobe and the saddle planes, and two pairs of streamwise vortices appear (a strong one, centred about the lobe, and a weaker one, coming from the previous dune, centred around the saddle). The distribution of the wall stress and the focal points of separation and attachment on the bed are discussed. The sensitivity of the average reattachment length, depends on the induced secondary flow, the streamwise and spanwise components of the channel resistance (the skin friction and the form drag), and the contribution of the form drag to the total resistance are also studied. Three-dimensionality of the bed increases the drag in the channel; the form drag contributes more than in the two-dimensional case to the resistance, except for the staggered-crest case. Turbulent-kinetic energy is increased in the separated shear layer by the introduction of three-dimensionality, but its value normalized by the plane-averaged wall stress is lower than in the corresponding two-dimensional dunes. The upward flow on the stoss side and higher deceleration of flow on the lee side over the lobe plane lift and broaden the separated shear layer, respectively, affecting the turbulent kinetic energy

Spatiotemporal bedload transport patterns over two-dimensional bedforms

Despite a rich history of studies investigating fluid dynamics over bedforms and dunes in rivers, the spatiotemporal patterns of sub-bedform bedload transport remain poorly understood. Previous experiments assessing the effects of flow separation on downstream fluid turbulent structures and bedload transport suggest that localized, intermittent, high-magnitude transport events (i.e., permeable splat events) play an important role in both downstream and cross-stream bedload transport near flow reattachment. Here, we report results from flume experiments that assess the combined effects of flow separation–reattachment and flow re-acceleration over fixed two-dimensional bedforms (1.7 cm high; 30 cm long). A high-speed camera observed bedload transport along the entirety of the bedform at 250 frames per second. Grain trajectories, grain velocities, and grain transport directions were acquired from bedload images using semiautomated particle-tracking techniques. Downstream and vertical fluid velocities were measured 3 mm above the bed using laser Doppler velocimetry (LDV) at 15 distances along the bedform profile. Mean downstream fluid velocity increases nonlinearly with increasing distance along the bedform. However, observed bedload transport increases linearly with increasing distance along the bedform, except at the crest of the bedform, where both mean downstream fluid velocity and bedload transport decrease substantially. Bedload transport time series and manual particle-tracking data show a zone of high-magnitude, cross-stream transport near flow reattachment, suggesting that permeable splat events play an essential role in the region downstream of flow reattachment.</p

Sensitivity of incipient particle motion to fluid flow penetration depth within a packed bed

A discrete element method is applied to a three-dimensional analysis related to sediment entrainment on a micro-scale. Sediment entrainment is the process by which a fluid medium accelerates particles from rest and advects them upward until they are either transported as bedload or suspended by the flow. Modelling of the entrainment process is a critically important aspect for studies of erosion, pollutant resuspension and transport, and formation of bedforms in environmental flows. Previous discrete element method studies of sediment entrainment have assumed the flow within the particle bed to be negligible and have only allowed for the motion of the topmost particles. At the same time, micro-scale experimental studies indicate that there is a small slip of the fluid flow at the top of the bed, indicating the presence of non-vanishing fluid velocity within the topmost bed layers. The current study demonstrates that the onset of particle incipient motion, which immediately precedes particle entrainment, is highly sensitive to this small fluid flow within the topmost bed layers. Using an exponential decay profile for the inner-bed fluid flow, the discrete element method calculations are repeated with different fluid penetration depths within the bed for several small particle Reynolds numbers. For cases with slip velocity corresponding to that observed in previous experiments with natural sediment, the predicted particle velocity is found to be a few percent of the fluid velocity at the top of the viscous wall layer, which is a reasonable range of velocities for observation of incipient particle motion. This method for prescribing the fluid flow within the particle bed allows for the current discrete element method to be extended in future studies to the analysis of sediment entrainment under the influence of events such as turbulent bursting. Additionally, predictions for the slip velocities and fluid flow profile within the bed suggest the need for further experimental studies to provide the data necessary for additional improvement of the discrete element method models. © 2009 The Authors. Journal compilation © 2009 International Association of Sedimentologists

Large-eddy simulation of two-dimensional dunes in a steady, unidirectional flow

We performed large-eddy simulations of the flow over a typical two-dimensional dune geometry at laboratory scale (the Reynolds number based on the average channel height andmean velocity is 18,900) using the Lagrangian dynamic eddy-viscosity subgrid-scale model. The results are validated by comparison with simulations and experiments in the literature. The flowseparates at the dune crest, generating a shear layer that plays a crucial role in the transport of momentum and energy, and the generation of coherent structures. The turbulent kinetic energy budgets show the importance of the turbulent transport and mean-flow advection in the bulk flow above the shear layer. In the recirculation zone and in the attached boundary layers production and dissipation are the most important terms. Large, coherent structures of various types can be observed. Spanwise vortices are generated in the separated shear layer due to the Kelvin-Helmholtz instability; as they are advected, they undergo lateral instabilities and develop into horseshoe-like structures, are tilted downward, and finally reach the surface. The ejection that occurs between the legs of the vortex creates the upwelling and downdrafting events on the free surface known as "boils." Near-wall turbulence, after the reattachment point, is affected by large streamwise Taylor-Görtler vortices generated on the concave part of the stoss side, which affect the distribution of the near-wall streaks

SPH modelling of depth-limited turbulent open channel flows over rough boundaries

A numerical model based on the Smoothed Particle Hydrodynamics (SPH) method is developed to simulate depth-limited turbulent open channel flows over hydraulically rough beds. The 2D Lagrangian form of the Navier-Stokes (N-S) equations are solved, in which a drag-based formulation is used based on an effective roughness zone near the bed to account for the roughness effect of bed spheres and an improved Sub-Particle-Scale (SPS) model is applied to account for the effects of turbulence. The SPS model is constructed based on the mixing-length assumption rather than the standard Smagorinsky approach to compute the eddy-viscosity. A more robust in/out-flow boundary technique is also proposed to achieve stable uniform flow conditions at the inlet and outlet boundaries where the flow characteristics are unknown. The model is applied to simulate uniform open channel flow over a rough bed composed of regular spheres and validated by experimental velocity data. To investigate the influence of the bed roughness on different flow conditions, data from 12 experimental tests with different bed slopes and uniform water depths are simulated and a good agreement has been observed between the model and experimental results of the streamwise velocity and turbulent shear stress. This shows that both the roughness effect and flow turbulence should be addressed in order to simulate the correct mechanisms of turbulent flow over a rough bed boundary and that the presented SPH model accomplishes this successfully

The impact of non-equilibrium flow on the structure of turbulence over river dunes

This piece of research expands our description of how rivers flow over dunes on a river bed. Most of the scientific communities' research to date has used unnaturally steady conditions to measure how water moves over dunes. Yet these flow conditions are not strictly true to the variety of conditions nature produces, most importantly during floods. This research is the first detailed description of a wide range of flow states over dunes, and changes our present understanding of the structure of flow over dunes in rivers. Consequently, the scientific community will be able to use this new information to better model and simulate how rivers work, how they flood, and how they transport sediment towards the worlds deltas