Optimal Grid Size Research Articles

Investigation into forces on offshore piles with constant and linearly varying diameters using CFD and extended Morison equation under separate wave and current loadings

This study presents a comparative analysis of hydrodynamic forces on cylindrical offshore piles with both constant and linearly varying diameters utilizing computational fluid dynamics (CFD) simulations. The classical Morison equation is evaluated alongside an extended version to address limitations in predicting forces on geometrically complex structures. Mesh convergence studies are performed to select the optimum grid size for separate wave and current simulations. The focus is on test cases characterized by small Keulegan-Carpenter (KC) numbers and relatively high Reynolds (Re) numbers within both inertia-dominated and diffraction zones. Numerical simulation results are utilized to compare the force predictions of the classical Morison equation and the extended Morison equation. It is observed that the classical Morison equation performs adequately for constant diameter piles, but it fails to predict forces on variable diameter piles accurately. In contrast, the extended Morison equation, incorporating nonlinear effects and variable cross-sections, provides significantly more accurate force predictions, particularly in the diffraction zone compared to the numerical simulations. This study emphasizes the critical importance of accounting for geometric variations, such as linearly varying pile diameters, under separate waves and currents loadings in hydrodynamic force calculations. These considerations support the development of enhanced design methods and optimization strategies, leading to safer and more efficient offshore structures.

Improving UASS pesticide application: optimizing and validating drift and deposition simulations.

As unmanned aerial spraying systems (UASS) usage grows rapidly worldwide, a critical research study was conducted to optimize the simulation of UASS applications, aiming to enhance pesticide delivery efficiency and reduce environmental impact. The study examined several key aspects for accurate simulation of UASS application with lattice Boltzmann method (LBM). Based on these discussions, the most suitable grid size and simulation parameters were selected to create a robust model for optimizing UASS performance in various pest management scenarios, potentially leading to more targeted and sustainable pest control practices. The effect of stability parameter, grid size around the rotor and near ground, and parameters at wake flow were carefully analyzed to improve the precision of pesticide drift predictions and deposition patterns. Optimal grid sizes were identified as 0.2 m generally, 0.025 m near rotors, and a 0.1 + 0.2 m scheme for ground proximity, with finer grids improving accuracy but increasing computation time. Wake resolution and threshold significantly influenced simulation results, while wake distance had minimal impact beyond a certain point. The LBM's accuracy was validated by comparing simulated downwash flow and droplet deposition with field test data. This study optimized UASS simulation parameters, balancing computational efficiency with accuracy. The validated model enhances our ability to design more effective UASS for pest management, potentially leading to more precise and targeted pesticide applications. These advancements contribute to the development of sustainable pest control strategies, aiming to reduce pesticide usage and environmental impact while maintaining crop protection efficacy. © 2024 Society of Chemical Industry.

Direct and mediated impacts of mixed forests on Norway spruce infestation by European bark beetle Ips typographus

Climate change-induced windfalls and droughts exacerbate bark beetle outbreaks, severely impacting forest ecosystems. Despite extensive research on bark beetle infestation patterns, the question regarding the optimal spatial grid (SG) size for analyzing this phenomenon remains unresolved. The protective potential of natural forest complexity against bark beetles has been underestimated. We used remotely sensed data to fit Generalized Linear Models and structural equation models to explore the direct and environment-mediated effects of mixed forest cover (MFC) on Norway spruce forest infestation in central Europe. We assessed the effectiveness of various spatial grids (from 100 m to 1 km) for studying infestation by Ips typographus. We found a strong non-linear decline in infestation with increasing MFC across different spatial scales. The relationship between infestation and temperature was positive, while elevation had a negative effect on infestation, with higher infestation rates observed below 900 m. Direct effects of environmental predictors on infestation were significant at SGs of 100 m, 300 m, 400 m, and 500 m, but insignificant at 200 m and 1000 m SGs. Slope positively influenced infestation at 300 m and 400 m SGs. MFC exhibited significant indirect effects on infestation mediated by elevation, temperature, potential evapotranspiration, slope, and heat load index. Landscape variables played a significant role in the models at high-resolution spatial grids, whereas climate variables were influential in models at lower spatial grids of infestation data. We argue that mixed forest facilitates cooling, preserves water, enriches symbiotic fungal community, alleviating tree drought stress and mitigating infestation risk. Broad-leave trees’ non-host volatiles presumably disrupt olfactory signals, impeding beetles’ ability to locate host trees effectively. Our results underscore the potential of increasing mixed forest cover as a self-sustainable silvicultural measure for forest protection against I. typographus and for mitigating the effects of climate change.

Multiscale modeling and thermal conductivity evaluation of nano-reinforced composite materials with pore defect

The performance of resin-based composite materials often exhibits diversity due to the designability of various components. Thermal conductivity, an important thermal parameter of the composite, plays a significant role in thermal-chemical reactions, thermal stress analysis, temperature conduction, etc. However, it is relatively difficult to experimentally explore the thermal conduction mechanism of hybrid composite materials, mainly due to the relatively difficult control of various components. Therefore, this paper proposes a sequentially coupled cross-scale numerical method to characterize the thermal conductivity of nano-reinforced composite materials with pores by a multiscale periodic Representative Volume Element model generated by an improved Random Sequential Absorption algorithm. Firstly, periodic temperature boundary conditions are described, and the thermal conductivity performances of nano-reinforced matrix and composite with pores are investigated based on the finite element homogenization theory. Then, the proposed modes are validated and grid sensitivity analysis is conducted, indicating that the optimal grid sizes for the RVE models are 1.9 nm for the nano-reinforced matrix and 0.14 μm for the composite with pores based on a comprehensive comparison of four pore characterization methods, respectively. Furthermore, the study explored the effect of multiple parameters including nanoparticle content, pore content, and pore shape on thermal conductivity. Numerical findings reveal that the thermal conductivity of the nanocomposite matrix exhibits a linear increase with higher particle content. Specifically, compared to 0 % particle content, the thermal conductivity rises by 141.92 % at 12 % particle content. While the composite material's transverse thermal conductivity is sensitive to porosity content, it is less influenced by pore shape. The method proposed in this paper provides an effective approach for studying the thermal conduction of nano-reinforced composite materials with pores, and the research findings also offer theoretical guidance for process engineers.

Numerical Analysis of Non-Fourier Model-Based Bio-Heat Transfer in the Laser-irradiated Axisymmetric Living Tissue.

The current work is related to the numerical investigation of non-Fourier heat transfer inside the short-pulsed laser-irradiated axisymmetric soft tissue phantom. It utilizes the modified discrete ordinate method to solve the transient radiative transfer equation (TRTE) for determining the intensity field. The laser energy absorbed by the soft tissue phantom behaves like a source in the Fourier/non-Fourier heat conduction model based-bio-heat transfer equation (BHTE), which is solved by employing the finite volume method (FVM) to determine the temperature distribution. Despite the prevalent use of non-Fourier BHTE for this purpose, a second law analysis is considered crucial to detect any potential anomalies. Equilibrium entropy production rates (EPR) are initially computed based on classical irreversible thermodynamics (CIT), which may yield negative values, possibly contravening the second law. Consequently, the EPR based on CIT is adjusted using the extended irreversible thermodynamics (EIT) hypothesis to ensure positivity. After that, the current research findings are compared with the results from the literature, and found good agreement between them. Then, the independent study is performed to select the optimum grid size, control angle size, and time step. A comparative analysis of results between the traditional Fourier and non-Fourier models has been performed. The impact of different parameters on the temperature fields and EPRs, is discussed. The effect of the optical properties of the inhomogeneity on the temperature distribution has been investigated. This study may help to enhance the effectiveness of the laser-based photo-thermal therapy.

Analytical review study of the Grid connected Micro grid Energy Management System

As an environmentally friendly method of distributing energy production, the integration of photovoltaic systems into micro grids has drawn in significant focus on. Our goal in doing is to examine features regarding micro grid that is linked to the power grid, with a focus on photovoltaic energy management in particular. Finding the optimal micro grid capacity for the solar system seeks to increase energy efficiency, decrease dependence on main grid, and promote an utilization of green power. The outlined optimization approach evaluates the micro grid’s dynamic interactions using state-of-the-art modelling and simulation tools. These components include photovoltaic panels, energy storage systems, alongside the main grid. The refinement method takes into account crucial factors including patterns of load demand, costs of the grid electricity, and variations in solar irradiation. Finding a happy medium between increasing the amount of power generated by renewable sources and decreasing overall energy costs is the objective. That study takes a multi-scenario approach to determining how various micro grid sizes affect overall system efficiency. Using scenario-based simulations and techno-economic criteria, the appropriate size of the photovoltaic system was determined. Factors like payback time, ROI, and system reliability are taken into account here. The study’s findings provide light on grid-connected micro grids, particularly in regards to photovoltaic energy management, which is crucial for their planning and implementation. In order to make educated decisions towards more robust and ecologically friendly power systems, stakeholders, lawmakers, and decision-makers can use the optimal micro grid size as a benchmark for future renewable power projects. This paper reviews the relevant literature and proposes a division and performance strategy based on its findings. By classifying energy management into three groups according to grid connection, configuration, and control method, this article provides a description of the performance, application, advantages, and disadvantages of algorithms that may be used as a reference for selecting an appropriate algorithm. Also included is a comparison table for the control strategies that were used to regulate a micro grid system that is connected to the grid.

Comparative analysis of turbulence model influence in numerical simulation of an experimental radial compressor stage

The accuracy of a CFD model of a turbo-machine might depend on a number of factors: turbulence model, quality of the mesh model, boundary conditions, solver settings, consideration of secondary geometric factors, etc. The purpose of this work is to develop practical recommendations for CFD calculations of centrifugal compressors based on the validation of a model of NASA High Efficiency Centrifugal Compressor experimental radial compressor stage. Results of a grid independence test are presented, and the optimal grid size for the High Efficiency Centrifugal Compressor stage is identified as comprising 3 million elements. CFD-calculations of an experimental stage were performed with different turbulence models. The obtained data was compared with the NASA experimental data considering integral (total pressure ratio, mass flow rate, adiabatic efficiency) and differential parameters (static pressure distribution downstream the vaned diffuser). The required CFD computational time for different turbulence models was calculated. Based on the results of this research, recommendations were formulated for the application of SST, k–ε, BSL EARSM and GEKO turbulence models for numerical modeling of centrifugal compressors.

Optimal grid size for site‐specific nutrient application

AbstractThis article develops a theoretical framework to determine the economically optimal grid size when sampling to guide precision application of inputs. Our theoretical model shows that a finer grid is optimal with increases in output price. A coarser grid is optimal with increased sampling costs and increased spatial correlation. With an exponential variogram, for example, the optimal grid size increases as the range increases. An applied example of lime application for winter wheat is used to demonstrate the framework. Spatial variograms for pH and Buffer pH were estimated using data from nine farmer fields. At the average spatial variability from these fields and using typical Oklahoma wheat yields of 40 bu/ac, grid sampling was economical when prices were above $5.43/bu. The optimal grid sizes were slightly larger than the 2.5‐acre sizes that are typically used by producers. The empirical example verified the theory in that it found that optimal grid size decreased with higher output prices and crop yields and increased with greater spatial correlation. For example, optimal grid size approximately doubled as the range of the exponential correlation function doubled.

Comparative Analysis of Debris Flow Numerical Simulation Based on the Difference between the Resolution of Topographic Information and Grid Size

In this study, a comparative analysis was conducted for the debris flow that occurred in Gokseong-gun, Jeollanam-do, in August 2020, using the difference between the resolution of topographic information and grid size. High-resolution topographic information (0.03 m) was established through photogrammetry. For comparison, the low-resolution topographic information was obtained from the contour lines of the 1:5000 digital map. The topographic information was depicted as a grid, with resolutions of 1, 5, and 10 m, and analyzed by setting the simulation grid size to 1, 5, and 10 m. According to the topographic resolution, no significant difference was obtained in the numerical simulation results, when high-resolution topographic information from UAV photogrammetry was used, and the analysis was similar to the actual debris flow. Additionally, when the size of the analysis grid for the simulation was 10 m, the simulation was very similar to the actual debris-flow situation. For predicting a risk area using a debris-flow model, it is very important to reflect actual information, such as topography, geology, and rainfall; technical parameters, such as the grid size, are also important. Moreover, determining the optimal grid size by considering the conditions of the study area, such as the basin area, is necessary.

Conjugate-Based Numerical Analysis of Parabolic Trough Receiver Pipe With Temperature-Dependent Thermo-Physical Properties of Heat Transfer Fluid Under Laminar Flow Regime

Abstract In this article, the use of gas as a working fluid in the parabolic trough receiver (PTR) has been investigated numerically. The present study aims to determine which gas will work best as a heat transfer fluid (HTF) by analyzing the impact of several gases on the PTR’s performance. So, gases, such as carbon dioxide, helium, nitrogen, oxygen, hydrogen, methane, neon, and air, are considered in the present study, which flow through a thick-wall stainless steel pipe under a laminar flow regime. The temperature-dependent thermo-physical properties of the gas are considered. The finite difference method (FDM) with the harmonic mean technique is employed to solve this conjugate heat transfer problem. The current research findings are verified with those reported in the literature and are in excellent agreement. The grid-independent study is conducted to choose the optimal grid size. After that, the multi-objective function optimization technique and performance enhancement factor (PEF) is used to select the best suitable HTF, and it found that hydrogen gas is most appropriate based on these two criteria. Then, the influence of various parametric studies such as Reynolds number, solar flux, and receiver pipe thickness on the Nusselt number has been carried out. It is found that the Nusselt number increases with the Reynolds number while it decreases with solar flux and receiver pipe thickness. The significance of the current study may aid in choosing the appropriate gas as HTF in the parabolic trough solar collector (PTSC).

Some considerations on the dependence to numerical schemes of Lagrangian radionuclide transport models for the aquatic environment

Lagrangian models present several advantages over Eulerian models to simulate the transport of radionuclides in the aquatic environment in emergency situations. A radionuclide release is simulated as a number of particles whose trajectories are calculated along time and thus these models do not require a spatial discretization (although it is always required in time). In this paper we investigate the dependence of a Lagrangian model output with the grid spacing which is used to calculate concentrations from the final distribution of particles, with the number of particles in the simulation and with the interpolation schemes which are required because of the discrete nature of the water circulation data used to feed the model. Also, a Lagrangian model may describe the exchanges of radionuclides between phases (liquid and solid), which is done in terms of transition probabilities. The dependence of these probabilities with time step is analyzed as well. It was found that the optimum grid size used to calculate concentrations should be carefully checked, and that temporal interpolation is more significant than spatial interpolation to obtain a more accurate solution. A method to estimate the number of particles required to have a certain accuracy level is proposed. Finally, it was found that for low sediment concentrations and small radionuclide kd, exact equations for the transition probabilities should be used; and that phase transitions introduce a stability condition as in Eulerian models.

Computational uncertainty and optimal grid size and time step of the Lax–Friedrichs scheme for the 1D advection equation

This paper examines truncation and round-off errors in the numerical solution of the 1D advection equation with the Lax–Friedrichs scheme, and accumulation of the errors as they are propagated to high temporal layers. The authors obtain a new theoretical approximation formula for the upper bound of the total error of the numerical solution, as well as theoretical formulae for the optimal grid size and time step. The reliability of the obtained formulae is demonstrated with numerical experimental examples. Next, the ratio of the optimal time steps under two different machine precisions is found to satisfy a universal relation that depends only on the machine precision involved. Finally, theoretical verification suggests that this problem satisfies the computational uncertainty principle when the grid ratio is fixed, demonstrating the inevitable existence of an optimal time step size under a finite machine precision.摘要本文对于应用Lax- Friedrichs 格式数值求解一维平流方程, 研究数值求解过程中产生的截断误差与舍入误差, 以及两种误差逐层向高时间层传播的累积, 得到新的数值解总误差上界的理论近似公式, 以及最优格距和最优时间步长的理论公式. 通过数值算例验证了所得公式的可靠性. 然后, 发现了两种不同机器精度下最优时间步长之比满足的一个仅与机器精度有关的普适关系. 最后, 理论验证了在网格比固定的情况下, 此问题满足数值计算的不确定性原理, 以及在机器有限精度下最优时间步长的必然存在.

Improved prediction of ion mobility for precipitators using FDM-FMG on fine computational domains

• FDM integrated with FMG method is a very fast convergent technique for solving the precipitator problem. • Gauss-Siedel is a perfect smoothing solver for FMG in terms of time performance. • Global optimal computational grid size is tracked and perfectly matched the experimental results. • Effective ion mobility is tracked at different applied voltages in precipitator with clean air. • FDM integrated with FMG is an effective technique in the early design stage of precipitators. This paper presents an improved approach for modelling electrostatic precipitators on one fine computational domain in clean air. Contrary to the previously published numerical techniques, the Finite Difference Method (FDM) integrated with Full Multi-grid method (FMG) is used to predict the optimal value of ion mobility at a certain applied voltage in precipitators. Three smoothing solvers for FMG are implemented including Gauss–Siedel, Successive Over Relaxation (SOR) and Successive Under Relaxation (SUR). Gauss–Siedel is examined against SOR and SUR on finer domains and it is found that Gauss–Siedel is greatly superior in terms of the timing performance. Two main ideas are discussed in this paper for the first time; the first idea is that the value of ion mobility is not constant for all applied voltages as published previously in the precipitators. The second one is predicting only one global optimal grid for solving Poisson and continuity equations that grantees both low truncation and round off errors that well matched the previously published experimental measurements more than that of the previously published numerical techniques. Moreover, the idea of tracking the optimal ion mobility and grid size gives the FDM-FMG the advantage of predicting an accurate picture for the electrical conditions in the early design of precipitators over the other numerical techniques. Finally, the FDM-FMG gives a more confident results for current density and voltage characteristics for precipitator which is proved by experiments.

Mapping fine-scale building heights in urban agglomeration with spaceborne lidar

The increasing availability of 3-D urban data yields new insights into urban developments and their implications for population density, energy consumption, and the carbon budget. However, existing products of urban building heights at a regional or global scale are mostly subject to coarse grid size or long-time lags. Fine-resolution building height maps remain unavailable for most regions to present recent vertical information. Also, the lack of sampled building heights with spatial and temporal consistency at larger scales makes it difficult to update building height maps. The newly available spaceborne lidar data from the Global Ecosystem Dynamics Investigation (GEDI) are expected to overcome these critical barriers. Here we propose a generalizable approach to mapping large-scale distributions of building heights by fusing GEDI-derived relative height metrics, optical data (i.e., Landsat-8 and Sentinel-2), and radar data (Sentinel-1). We applied our approach to the Yangtze River Delta region (YRD), one of China's largest urban agglomerations. We investigated the availability of building height samples generated from GEDI-based relative height metrics and the optimal grid size of building height mapping into 30-m (about footprint level) and 150-m (regional level) grid sizes. We finally developed a random forest model using active and passive sensors to extrapolate GEDI-derived samples discretely to the continuous building height map at the 150-m grid size in 2019. We revealed the spatial distribution patterns of building heights and the urbanization effect on the city's mean building heights in the YRD region. We found that: (1) GEDI-derived building height samples were highly consistent with the reference building height data at the footprint (i.e., Pearson's r = 0.86, RMSE = 9.25 m, n = 237) and regional (i.e., Pearson's r = 0.76, RMSE = 6.36 m, n = 69) levels. (2) The Pearson's correlation coefficient (r) and root mean square error (RMSE) of the final spatially continuous and up-to-date building height map were 0.85 and 5.03 m, respectively. (3) The resulting map showed a strong positive correlation between the city's mean building height and urbanization level. Our work makes it possible to use remotely sensed data to make global maps of building heights at a 150-m scale.

An improved approach to estimating crop lodging percentage with Sentinel-2 imagery using machine learning

It is imperative to rapidly and precisely acquire crop lodging area and severity for disaster prevention and yield prediction. However, estimation of crop lodging area at a large scale remains challenging due to the relatively low sensitivity of remote sensing signal to the lodging variation, limited availability of remote sensing images, and lodging statistical data. This study proposes a new method for lodging area estimation based on the optimal grid cell of Sentinel-2 and crop lodging percentage, overcoming the limitation of traditional pixel-based mapping approaches that fail to obtain quantitative lodging information. Basing the spatial aggregation method, we analyzed the optimal grid size of Sentinel-2 data for lodging percentage estimation. Then we investigated the spectral response for different lodging percentage levels and analyzed the potential of lodging percentage estimation for Sentinel-2 metrics (including selected spectral bands and their derived vegetation indexes (VIs)). A quantitative model was established between the training set and the Sentinel-2 metrics using the random forest (RF) algorithm. Finally, around 1462.62 ha fields from six counties or districts in Heilongjiang province in China were estimated for lodging percentage. Results indicate that the proposed method can estimate the crop lodging percentage on the testing set with an R2 and RMSE of 0.64 and 25.24, respectively, which can explain around 95 % spatial variation of lodging crop. Moreover, the overall magnitude of reflectance increased with the increase in lodging percentage. Among all Sentinel-2 optimal metrics, the Green, SWIR1, and Red edge 1 bands are the most crucial indicators for lodging percentage estimation. Our results on lodging percentage estimation in the study area indicate that there is more lodging maize in the Meilisidawoerzu district than in other areas. Although typhoons passed over Fuyu and Lindian counties, the lodging percentage in these areas is relatively low. The lodging percentage map has great value in agriculture management and insurance claim.

Numerical Study of Scale Effects on Open Water Propeller Performance

The present study aims to investigate the scale effects of the open water propeller performance using computational fluid dynamics (CFD). The results are presented for the propeller which was previously 3D scanned and digitized. The results obtained using two turbulence models within the numerical simulations are compared. The verification study is conducted to assess the numerical uncertainty and thus obtain the optimal grid size for the numerical simulations. A transition model is used at the model scale to account for the partially laminar flow. The propeller is then scaled, and numerical simulations are performed to assess the scale effects on the open water performance of the considered propeller. The results demonstrate the significant scale effects on open water characteristics however, scale effects are considerably lower when the transition model is applied within the numerical simulations at the model scale.

Charging Station Distribution Optimization Using Drone Fleet in a Disaster

A disaster is an unforeseen calamity that can cause damage to properties and can bring about a loss of human lives. Usually, many relief supplies, such as clean water, food, and medical supplies, are required by disaster victims. Quick response and rapid distribution of essential relief items into the affected region can save countless lives and prevent or slow down the effects of disasters. In this regard, disaster management comes into play, which is highly dependent on the topography and access of the disaster-hit area. If the disaster-hit site has little or no road connectivity, the use of UAVs/drones becomes essential in delivering health packages to the affected areas to assist with humanitarian aid. Since the battery capacity of the drone is limited, UAVs/drones require charging stations located at various places to carry out the necessary relief work. These charging stations should be transported using road infrastructure and preinstalled in disaster-prone areas, as access to these areas may be denied once the disaster hits. This article presents a novel optimization model to distribute relief items to disaster-hit areas. The objective of this model is to optimize the location and the number of the charging stations. We consider the relative priority of locations where a preference is given to locations with higher priority levels. The optimal number of charging stations and optimal routes has also been determined by using our optimization model. To illustrate the use of our model, numerical examples have been simulated for a different number of targets. Through our numerical simulation, it was observed that the drone’s maximum distance capacity is the key factor in determining the optimal grid size, which directly correlates to the number of charging stations.

Charging Stations Distribution Optimization using Drones Fleet for Disaster Prone Areas

A disaster is an unforeseen calamity that causes damage to property or brings about a loss of human life. Quick response and rapid distribution of vital relief items into the affected region could save precious lives. In this regard, disaster management comes into play, which is highly dependent on the topography of the disaster-hit area. If the disaster-hit area has little or no road connectivity, the use of drones in such areas becomes essential for the delivery of health packages. Since the battery capacity of the drone is limited, there is a need of charging stations that should be transported using road infrastructure and pre-installed in disaster-prone areas, as access to these areas may be denied once the disaster hits. In this article, a simulation model was used to optimize the number and location of drone charging stations for deployment in a disaster-prone area in the pre-disaster scenario, aiming at the distribution of relief items to disaster-hit areas in the post-disaster scenario. We consider the relative priority of locations where a preference is given to the locations that have higher priority levels. An optimal number of charging stations and optimal routes have also been determined by using our optimization model. To illustrate the use of our model, numerical examples have been simulated for different sizes of the disaster-hit area and the number of targets. In our numerical simulation, it was observed that the drone's maximum distance capacity is the key factor in determining the optimal grid size, which directly correlates to the number of charging stations.

Energy efficient grid based k‐means clustering algorithm for large scale wireless sensor networks

SummaryHierarchical based routing is a kind of group‐based routing that consists in creating of a virtual hierarchy among network sensor nodes. This class of routing technique is generally designed for large‐scale networks. It aims to efficiently increase network lifetime by cutting the whole network into clusters. However, traditional clustering techniques show some limitations and do not take into consideration the self‐organized with dynamic topology inherent in wireless sensor networks (WSNs). These limitations can lead to an unbalanced cluster head distribution that affects the whole network energy consumption. In this paper, we propose a grid‐based k‐means clustering protocol (named GBK), which combines grid‐based routing with k‐means algorithm in order to overcome the above mentioned weaknesses. From the supervised zone area size parameter, the base station determines the optimal grid size based on our optimization study. Afterwards, the k‐means algorithm is executed in every grid cell generating a cluster head per cell grid where the nearest node to the grid cell centroid is elected. An enhancement of this proposed GBK algorithm named GBK‐R is also proposed to extend network stability of the GBK algorithm by node scoring calculation that take as parameters the node remaining energy in addition to the distance to centroid. Our proposed GBK and GBK‐R algorithms allow for an enhanced network stability and increase the network lifetime as demonstrated by our performance evaluation study. In addition, this GBK clustering algorithm provides a better network topology control and a better control of the random nature of node distribution by generating cluster heads with bounded localization.

Analysis of the gallium melting problem with different heating configurations

A moving boundary problem is numerically investigated with gallium substance and FVM (finite volume method). Following the determination of the optimal grid size and time-step, a natural convection problem in a vertical slot is studied to validate the multi-cellular melting front. Different heating configurations are modelled to understand the solid-liquid phase change phenomenon under different scenarios for the gallium melting problem. These different scenarios include spatial differential heating (sinusoidal), temporal differential heating (pulsating), inclination angle, and MHD conditions. It is found that grid independence study should not be conducted with liquid fraction or similar average value. If the first time-step is larger than 0.1 s, early development of the Bénard cells will not be captured accurately, even when the outer iterations converge. It is also observed that if peak point of differential heating is close to the top of the domain, melting front will progress faster. When Lorentz force is active, at high Hartmann numbers, oscillation of the Nusselt number is dampened.