Lagrangian Particle Simulations Research Articles

Hybrid large eddy simulation and Lagrangian simulation of a compressible turbulent planar jet with a chemical reaction

AbstractLarge eddy simulation (LES) coupled with Lagrangian particle simulation (LPS) is applied to investigate high‐speed turbulent reacting flows. Here, LES solves a velocity field while LPS solves scalar transport equations with notional particles. Although LPS does not require sub‐grid scale models for chemical source terms, molecular diffusion has to be modeled by a so‐called mixing model, for which a mixing volume model (MVM), that is originally proposed for an inert scalar in incompressible flow, is extended to reactive scalars in compressible flows. The extended model is based on a relaxation process toward the average of nearby notional particles and assumes a common mixing timescale for all species. LES/LPS with the MVM is applied to a temporally‐evolving compressible turbulent planar jet with an isothermal reaction and is tested by comparing the results with direct numerical simulation (DNS). The results show that LES/LPS well predicts the statistics of mass fractions. As the jet Mach number increases, the reaction progress delays due to the delayed jet development. This Mach number dependence is also well reproduced in LES/LPS. The mean molecular diffusion term of the product calculated as a function of its mass fraction also agrees well between LES/LPS and DNS. An important parameter for the MVM is the distance among particles, for which the requirement for accurate prediction is presented for the present test case. LES/LPS with the MVM is expected to be a promising method for investigating compressible turbulent reactive flows at a moderate computational cost.

Pre-asymptotic dispersion of active particles through a vertical pipe: the origin of hydrodynamic focusing

When motile algal cells are exposed to gyrotactic torques, their swimming directions are guided to form radial accumulation, well known as hydrodynamic focusing. The origin of hydrodynamic focusing from the effects of active swimming, ambient flow and particle anisotropy is elucidated in the present study on the pre-asymptotic dispersion of active particles through a vertical pipe. With an extension of the Galerkin method to pipe flows, time-dependent solutions directly from the Smoluchowski equation in the position and orientation space are derived by series expansions of spherical harmonics and Bessel functions. Ballistic and diffusive scaling laws are examined with the predominance of self-propelled swimming, and computation is validated against an explicit benchmark solution and Lagrangian particle simulation. In the limit of extreme shear, the competitive roles of shear dispersion and Brownian rotation are reflected concretely in the pre-asymptotic phase of hydrodynamic focusing. For flows with various shear strengths, a concentration peak in near-wall regions with a smooth transition to hydrodynamic focusing is illustrated with richer phenomena in upwelling and downwelling flows. A newly observed regime through a vertical pipe, named transient effective trapping, is revealed as a transitional mode towards hydrodynamic focusing. The pre-asymptotic approach to hydrodynamic focusing is elaborated intensively through extensive solutions of concentration moments and macroscopic transport coefficients characterised by swimming and flow Péclet numbers. The unique findings for the origin of hydrodynamic focusing could provide insight into related micro-algae reactor technology and contribute to flow control and biomass transfer in confined environments.

Efficiently simulating Lagrangian particles in large-scale ocean flows — Data structures and their impact on geophysical applications

Studying oceanography by using Lagrangian simulations has been adopted for a range of scenarios, such as the determining the fate of microplastics in the ocean, simulating the origin locations of microplankton used for palaeoceanographic reconstructions, and for studying the impact of fish aggregation devices on the migration behaviour of tuna. These simulations are complex and represent a considerable runtime effort to obtain trajectory results, which is the prime motivation for enhancing the performance of Lagrangian particle simulators. This paper assesses established performance enhancing techniques from Eulerian simulators in light of computational conditions and demands of Lagrangian simulators. A performance enhancement strategy specifically targeting physics-based Lagrangian particle simulations is outlined to address the performance gaps, and techniques for closing the performance gap are presented and implemented. Realistic experiments are derived from three specific oceanographic application scenarios, and the suggested performance-enhancing techniques are benchmarked in detail, so to allow for a good attribution of speed-up measurements to individual techniques. The impacts and insights of the performance enhancement strategy are further discussed for Lagrangian simulations in other geoscience applications. The experiments show that I/O-enhancing techniques, such as dynamic loading and buffering, lead to considerable speed-up on-par with an idealised parallelisation of the process over 20 nodes. Conversely, while the cache-efficient structure-of-arrays collection yields a visible speed-up, other alternative data structures fail in fulfilling the theoretically-expected performance increase. This insight demonstrates the importance of good data alignment in memory and caches for Lagrangian physics simulations.

Lagrangian particle simulation of hydrogen pellets and SPI into runaway electron beam in ITER

Numerical studies of the ablation of pellets and shattered pellet injection (SPI) fragments into a runaway electron beam in ITER have been performed using a time-dependent pellet ablation code [Samulyak et al., Nucl. Fusion, 61(4), 046007 (2021)]. The code resolves detailed ablation physics near pellet fragments and large-scale expansion of ablated clouds. The study of a single-fragment ablation quantifies the influence of various factors, in particular, the impact ionization by runaway electrons and cross-field transport models, on the dynamics of ablated plasma and its penetration into the runaway beam. Simulations of SPI performed using different numbers of pellet fragments study the formation and evolution of the ablation clouds and their large-scale dynamics in ITER. The penetration depth of the ablation clouds is found to be of the order of 50 cm.

Three-dimensional hydrodynamic modelling of the Moroccan Atlantic coast: A case study of Agadir bay

Coastal areas are a noteworthy source of commercial and economic fortunes for surrounding municipalities throughout the Moroccan Atlantic coast. Thus, a deep knowledge of local hydrodynamics and environmental processes associated is integral to effective coastal management. 3D hydrodynamic model that includes a Lagrangian particle simulation can participate to this understanding of dynamics. The model was calibrated and validated against meteorological conditions, sea surface level, harmonic tidal constituents, water temperature and salinity using a combination of available in-situ measurements, satellite, and ARGO floats data. Subsequently, it was used to determine the pathway of passive tracers and estimate the local residence time (RT). Despite some discrepancies, the findings revealed a good match between simulations and observations, which underlines the feasibility of the model in predicting the main dynamic features of the Agadir bay. Overall, the hydrodynamics of the area is tidal dominated by semidiurnal tides (M2) and governed by westerly and northwesterly winds. Passive tracer simulations showed strong seasonal and spatial variability, conditioning the obtained RTs, with mean values much shorter during summer (3 to 9 days) than winter (5 to 15 days). The tracers look to be trapped inside a coastal cyclonic eddy that increases the RTs in the southern bay, making it an area with highest likelihood of accumulation of pollutants while favoring the northward transport and decrease RTs in the northern bay.

Influence of Indo-Pacific ocean currents on the distribution and demographic patterns of the brown seaweed Sargassum polycystum in tropical east Asia

Long-distance drifting of seaweeds driven by ocean currents is an ideal model for exploring population-level genetic connectivity and phylogeographic structure. In the Indo-Pacific convergence region, we integrated phylogeographic and ocean current data and Lagrangian particle simulations to explore how the ocean currents contributed to the biogeographical patterns and population genetic connectivity of Sargassum polycystum. The oceanographic transport and direction of gene flow was in line with contemporary ocean currents. The S. polycystum geographical dispersal from glacial refugia homogenized the footprint of genetic divergence. The multidisciplinary intersection provides insights into the evolutionary history and biogeographic conservation of tropical seaweeds in the Indo-Pacific convergence region.

Solute dispersion in channels with periodic square boundary roughness

Transport of solutes through channels with rough boundaries is abundant in natural and engineered settings. However, it is not known currently what the consequences of an abruptly alternating boundary are for the solute dispersion, in particular when advected by inertial fluid flow. To investigate this, we compute numerically the time-asymptotic longitudinal dispersion coefficient of a passive solute advected by fluid flow through a two-dimensional channel with square boundary roughness. We determine how the effective diffusion coefficient depends on the boundary amplitude, Péclet number and Reynolds number. For creeping flow, the effective diffusion coefficient is found to be enhanced significantly through the recirculation zones. Increasing fluid inertia reduces the effective diffusion coefficient by up to a factor of two for high Péclet numbers. We interpret this behaviour by analysing residence times computed from Lagrangian particle simulations.

Coastal circulation and water transport properties of the Red Sea Project lagoon

The Red Sea Project (RSP) is based on a coastal lagoon with over 90 pristine islands. The project intends to transform the Red Sea coast into a world-class tourist destination. To better understand the regional dynamics and water exchange scenarios in the lagoon, a high-resolution numerical model is implemented. The general and tidal circulation dynamics are then investigated with a particular focus on the response of the lagoon to strong wind jets. Significant variations in winter and summer circulation patterns are identified. The tidal amplitude inside the lagoon is greater than that outside, with strong tidal currents passing over its surrounding coral reef banks. The lagoon rapidly responds to the strong easterly wind jets that occur mainly in winter; it develops a reverse flow at greater depths, and the coastal water elevation is instantly affected. Lagrangian particle simulations are conducted to study the residence time of water in the lagoon. The results suggest that water renewal is slow in winter. Analysis of the Lagrangian coherent structures (LCS) reveals that water renewal is largely linked to the circulation patterns in the lagoon. In winter, the water becomes restricted in the central lagoon with only moderate exchange, whereas in summer, more circulation is observed with a higher degree of interaction between the central lagoon and external water. The results of LCS also highlight the tidal contribution to stirring and mixing while identifying the hotspots of the phenomenon. Our analysis demonstrates an effective approach for studying regional water mixing and connectivity, which could support coastal management in data-limited regions.

Water exchange between the inner and outer archipelago areas of the Finnish Archipelago Sea in the Baltic Sea

We studied the water age and transport of passive tracers in the Archipelago Sea, Baltic Sea, using the COHERENS 3D hydrodynamic model and the OpenDrift Lagrangian particle model. The mean water age, which was calculated with COHERENS over a period of 6 years, varied between 1 and 3 months in the outer archipelago and between 3 and 6 months in the middle archipelago. The water age was highest in the inner archipelago, up to 7 months. As the density stratification is weak in large parts of this area, except for the seasonal thermocline, significant differences in the water age between the surface and bottom layers were seen only in the river mouths and in the deep channels of the middle archipelago. The Lagrangian particle simulations showed that the middle archipelago is more open towards the north than south. From the northern boundary, the Bothnian Sea, the largest transport to the middle archipelago occurred with NW winds. Due to the geometry and density of the islands in the area, the prevailing wind direction, SW, alone is not optimal for transporting tracer particles to the middle archipelago. From the southern boundary, the Baltic Proper, transport to the middle archipelago occurred mainly with SE winds and during events when the wind direction shifted from SW to SE or vice versa. The transport further into the inner archipelago was limited to only a few cases, indicating that the inner archipelago is fairly sheltered from transport from the outer archipelago.

Higher-order nonlocal theory of Updated Lagrangian Particle Hydrodynamics (ULPH) and simulations of multiphase flows

In this work, we present a higher-order nonlocal continuum theory of a recently developed updated Lagrangian particle hydrodynamics (ULPH) (see: Tu and Li, 2017 and Yan et al., 2019) and its applications to multiphase flows. The original nonlocal differential operators used in ULPH have only the first-order accuracy, and they may not be able to simulate some complicated and delicate three-dimensional flow problems. In order to improve the computational accuracy and stability, we adopt the nonlocal synchronized differential operator from the reproducing kernel particle method (RKPM), which is regarded as the higher-order nonlocal differential operator, and we apply them to build higher-order ULPH formulations. The main advantage of the higher-order nonlocal differential operator over the original one is its high accuracy in unstructured particle distribution, and it is fully controlled by the approximation polynomial basis.Numerical verifications have been carried out to validate the accuracy of the proposed approach by using various polynomial bases. Several challenging and delicate three-dimensional multiphase flow benchmark problems are solved to demonstrate the capability of the proposed method. The numerical results of the higher-order ULPH show good agreement with theoretical and numerical solutions in the literature, demonstrating the promising potential of higher-order nonlocal ULPH formulation in modeling and simulating multiphase flows with substantial topological variations of interfaces and high density ratios.

Rejection of the genetic implications of the \u201cAbundant Centre Hypothesis\u201d in marine mussels

The ‘Abundant-Centre Hypothesis’ is a well-established but controversial hypothesis stating that the abundance of a species is highest at the centre of its range and decreases towards the edges, where conditions are unfavourable. As genetic diversity depends on population size, edge populations are expected to show lower intra-population genetic diversity than core populations, while showing high inter-population genetic divergence. Here, the genetic implications of the Abundant-Centre Hypothesis were tested on two coastal mussels from South Africa that disperse by means of planktonic larvae, the native Perna perna and the invasive Mytilus galloprovincialis. Genetic structure was found within P. perna, which, together with evidence from Lagrangian particle simulations, points to significant reductions in gene flow between sites. Despite this, the expected diversity pattern between centre and edge populations was not found for either species. We conclude that the genetic predictions of the Abundant-Centre Hypothesis are unlikely to be met by high-dispersal species with large population sizes, and may only become evident in species with much lower levels of connectivity.

Updated Lagrangian Particle Hydrodynamics (ULPH) modeling and simulation of multiphase flows

In this paper, a weakly compressible updated Lagrangian particle hydrodynamics (ULPH) model [1] has been developed for multiphase flows with high density ratios and viscosity ratios. To enhance computation stability and prevent penetrations near the multiphase flow interface, a new surface tension resultant formulation based on the Continuum Surface Force (CSF) formulation [2], combined with the interface sharpness force, is also developed within the framework of ULPH method. The intermediate configuration is considered in the computational algorithm, and a modified predictor-corrector scheme is adopted to solve governing equations, which significantly improve the accuracy and efficiency of the ULPH model. Several numerical examples are presented to compare with either analytical or computational results obtained by using different numerical methods such as Smoothed Particle Hydrodynamics (SPH) method, Moving Particle Semi-implicit (MPS) method and Level Set (LS) method within the framework of Finite Element Method (FEM). The results indicate that the ULPH method has good accuracy, stability, and convergence properties in simulations of multiphase flows.

Supervised parallel-in-time algorithm for long-time Lagrangian simulations of stochastic dynamics: Application to hydrodynamics

Lagrangian particle methods based on detailed atomic and molecular models are powerful computational tools for studying the dynamics of microscale and nanoscale systems. However, the maximum time step is limited by the smallest oscillation period of the fastest atomic motion, rendering long-time simulations very expensive. To resolve this bottleneck, we propose a supervised parallel-in-time algorithm for stochastic dynamics (SPASD) to accelerate long-time Lagrangian particle simulations. Our method is inspired by bottom-up coarse-graining projections that yield mean-field hydrodynamic behavior in the continuum limit. Here as an example, we use the dissipative particle dynamics (DPD) as the Lagrangian particle simulator that is supervised by its macroscopic counterpart, i.e., the Navier-Stokes simulator. The low-dimensional macroscopic system (here, the Navier-Stokes solver) serves as a predictor to supervise the high-dimensional Lagrangian simulator, in a predictor-corrector type algorithm. The results of the Lagrangian simulation then correct the mean-field prediction and provide the proper microscopic details (e.g., consistent fluctuations, correlations, etc.). The unique feature that sets SPASD apart from other multiscale methods is the use of a low-fidelity macroscopic model as a predictor. The macro-model can be approximate and even inconsistent with the microscale description, but SPASD anticipates the deviation and corrects it internally to recover the true dynamics. We first present the algorithm and analyze its theoretical speedup, and subsequently we present the accuracy and convergence of the algorithm for the time-dependent plane Poiseuille flow, demonstrating that SPASD converges exponentially fast over iterations, irrespective of the accuracy of the predictor. Moreover, the fluctuating characteristics of the stochastic dynamics are identical to the unsupervised (serial in time) DPD simulation. We also compare the performance of SPASD to the conventional spatial decomposition method, which is one of the most parallel-efficient methods for particle simulations. We find that the parallel efficiency of SPASD and the conventional spatial decomposition method are similar for a small number of computing cores, but for a large number of cores the performance of SPASD is superior. Furthermore, SPASD can be used in conjunction with spatial decomposition for enhanced performance. Lastly, we simulate a two-dimensional cavity flow that requires more iterations to converge compared to the Poiseuille flow, and we observe that SPASD converges to the correct solution. Although a DPD solver is used to demonstrate the results, SPASD is a general framework and can be readily applied to other Lagrangian approaches including molecular dynamics and Langevin dynamics.

Stochastic Lagrangian particle simulation of air pollution dynamic at mountain base and vicinity

In this work, we investigated the effect of horizontal turbulent diffusion coefficients on the pollution accumulation and distribution near the mountain. The diffusion coefficients, corresponding to variation of wind and particle flow, were considered in three different functions, which are constant, linear decay, and exponential decay function, in governing main simplified cases. In the calculation, the transport of pollution was performed using Lagrangian particle models. The results show that the characteristics of pollution distribution were given by how diffusion coefficients are functioned. Specifically, the non-variant of turbulent diffusion coefficient causes the pollution concentration to get highly accumulated close to the mountain boundary. However, the higher magnitude in non-variant diffusion coefficients allows more turbulences and reflect the highest pollution concentration to step away from the mountain base. Nevertheless, for diffusion coefficient in variant version, the pollution distribution characteristic lies between the low and high non-variant limits, caused by the decay of the diffusion coefficients away from the mountain. However, the exponential decay tends to spread the pollution further out than that of the linear decay due to the abrupt drop of the diffusion coefficients.

Size distribution spectrum of noninertial particles in turbulence.

Collision-coalescence growth of noninertial particles in three-dimensional homogeneous isotropic turbulence is studied. Smoluchowski's coagulation equation describes the evolution of the size distribution of particles in this system. By applying a methodology based on turbulence theory, the equation is shown to have a steady-state solution, which corresponds to the Kolmogorov-type power-law spectrum. Direct numerical simulations of turbulence and Lagrangian particles are conducted. The result shows that the size distribution in a statistically steady state agrees accurately with the theoretical prediction.

Evidence for rangewide panmixia despite multiple barriers to dispersal in a marine mussel

Oceanographic features shape the distributional and genetic patterns of marine species by interrupting or promoting connections among populations. Although general patterns commonly arise, distributional ranges and genetic structure are species-specific and do not always comply with the expected trends. By applying a multimarker genetic approach combined with Lagrangian particle simulations (LPS) we tested the hypothesis that oceanographic features along northeastern Atlantic and Mediterranean shores influence dispersal potential and genetic structure of the intertidal mussel Perna perna. Additionally, by performing environmental niche modelling we assessed the potential and realized niche of P. perna along its entire native distributional range and the environmental factors that best explain its realized distribution. Perna perna showed evidence of panmixia across >4,000 km despite several oceanographic breaking points detected by LPS. This is probably the result of a combination of life history traits, continuous habitat availability and stepping-stone dynamics. Moreover, the niche modelling framework depicted minimum sea surface temperatures (SST) as the major factor shaping P. perna distributional range limits along its native areas. Forthcoming warming SST is expected to further change these limits and allow the species to expand its range polewards though this may be accompanied by retreat from warmer areas.

Comparisons and applications of four independent numerical approaches for linear gyrokinetic drift modes

To help reveal the complete picture of linear kinetic drift modes, four independent numerical approaches, based on the integral equation, Euler initial value simulation, Euler matrix eigenvalue solution, and Lagrangian particle simulation, respectively, are used to solve the linear gyrokinetic electrostatic drift mode equation in Z-pinch with slab simplification and in tokamak with a ballooning space coordinate. We identify that these approaches can yield the same solution with the difference smaller than 1%, and the discrepancies mainly come from the numerical convergence, which is the first detailed benchmark of four independent numerical approaches for gyrokinetic linear drift modes. Using these approaches, we find that the entropy mode and interchange mode are on the same branch in Z-pinch, and the entropy mode can have both electron and ion branches. And, at a strong gradient, more than one eigenstate of the ion temperature gradient mode (ITG) can be unstable and the most unstable one can be on non-ground eigenstates. The propagation of ITGs from ion to electron diamagnetic direction at strong gradient is also observed, which implies that the propagation direction is not a decisive criterion for the experimental diagnosis of turbulent mode at the edge plasmas.

Oceanographic Conditions Limit the Spread of a Marine Invader along Southern African Shores.

Invasive species can affect the function and structure of natural ecological communities, hence understanding and predicting their potential for spreading is a major ecological challenge. Once established in a new region, the spread of invasive species is largely controlled by their dispersal capacity, local environmental conditions and species interactions. The mussel Mytilus galloprovincialis is native to the Mediterranean and is the most successful marine invader in southern Africa. Its distribution there has expanded rapidly and extensively since the 1970s, however, over the last decade its spread has ceased. In this study, we coupled broad scale field surveys, Ecological Niche Modelling (ENM) and Lagrangian Particle Simulations (LPS) to assess the current invaded distribution of M. galloprovincialis in southern Africa and to evaluate what prevents further spread of this species. Results showed that all environmentally suitable habitats in southern Africa have been occupied by the species. This includes rocky shores between Rocky Point in Namibia and East London in South Africa (approx. 2800 km) and these limits coincide with the steep transitions between cool-temperate and subtropical-warmer climates, on both west and southeast African coasts. On the west coast, simulations of drifting larvae almost entirely followed the northward and offshore direction of the Benguela current, creating a clear dispersal barrier by advecting larvae away from the coast. On the southeast coast, nearshore currents give larvae the potential to move eastwards, against the prevalent Agulhas current and beyond the present distributional limit, however environmental conditions prevent the establishment of the species. The transition between the cooler and warmer water regimes is therefore the main factor limiting the northern spread on the southeast coast; however, biotic interactions with native fauna may also play an important role.

Computational analysis of insect impingement patterns on wind turbine blades

AbstractWind turbines experience significant power loss due to insect contamination on the blades. In order to estimate power losses, computational fluid dynamics software or empirical models are used to compute drag increases due to roughness‐induced boundary‐layer transition. These models require knowledge of the expected levels and location of insect contamination on the blade surface. This is generally unknown, making power loss predictions unreliable. The present study develops a computer simulation to predict this information and uses this tool to simulate insect impingement for a variety of turbine operating conditions. The simulation code combines an invsicid panel method with a Lagrangian insect particle simulation module to first solve for the turbine velocity field and then track insect paths through this field. The effects of blade thickness, angle of attack and insect size are studied for 2D airfoil sections. The simulations show that increasing blade thickness leads to a larger chordwise extent of insect impingement yet lower maximum levels of contamination. Increasing insect mass is also found to increase the chordwise extent of impingement. These results are consistent with previous wind tunnel results and theoretical predictions. The model is then applied to a representative 5‐MW turbine model to determine spanwise variation in contamination. Results agree qualitatively with field observation, suggesting that this technique may be used in the future to more accurately predict power losses on turbines. Copyright © 2015 John Wiley & Sons, Ltd.

Particle simulation and flow sequence on drainage of liquid particles

The emptying efficiency/depletion ratio firstly proposed by Hanin (1999) [7] has proven analytically that tanks with cross-sectional area expressed in the form of a higher-order polynomial of the liquid head (denoted as higher-order tank in this paper) are effective in reducing the efflux time. In this study, a Lagrangian particle method (moving particle semi-implicit (MPS) method) is used to simulate the draining process of water particles in tanks of various geometries (n-order tank), mainly to improve the physical understanding on why higher-order tanks are more effective in draining water particles. Analytically, it is shown that the reduction in efflux time is associated with the decrease of J-factor introduced in this paper. It can be proven that there exists a theoretical minimum of the J-factor (hence the efflux time) as the order (n) approaches infinity. In cases where the deformation of the free surface is mild while draining, the predicted time evolution of the water head agrees quite well with that of Torricelli’s law. Generally, the simulated averaged discharge coefficient increases with the order of the shape function used to describe the cross-sectional area of the tank, which may explain the effectiveness of higher-order tanks. From the Lagrangian particle simulation, the use of the flow sequence technique has revealed that water particles with identical range of drainage time form an inverted U-band (draining layer) in lower-order tanks. Interestingly, as the order (n) increases, flattening of such draining layers is observed and this has led to a reduction of efflux time of water particles especially for those near the side-walls.