Efficient Simulation Model Research Articles

Implementation and validation of a very-high-energy electron model in the matRad treatment planning system.

While electron beams of up to 20 MeV are commonly used in radiotherapy, the use of very-high-energy electrons (VHEEs) in the range of 100-200 MeV is now becoming a realistic option thanks to the recent advancements in accelerator technology. Indeed, VHEE offers several clinically attractive features and can be delivered using various conformation methods (including scanning, collimation, and focussing) at ultra-high dose rates. To date, there is a lack of research tools for fast simulation of treatment plans using VHEE beams. This work aims to implement and validate a simple and fast dose calculation algorithm based on the Fermi-Eyges theory of multiple Coulomb scattering for VHEE radiation therapy, with energies up to 200 MeV. A treatment planning system (TPS) toolkit with VHEE modality would indeed allow for further preclinical investigations, including treatment plan optimization and evaluation, and thus contribute to the gradual introduction of VHEE radiotherapy in clinical practice. A VHEE pencil beam scanning double Gaussian model was introduced into the open-source TPS matRad environment along with new functions and options dedicated to VHEE dose calculations. Various geometries and field configurations were then calculated in matRad (up to 200 MeV and 15×15 cm2, with complex bone or lung heterogeneities) and the results were compared to Monte Carlo simulations in the TOPAS/Geant4 toolkit. Two types of beam model (divergent or focused) were also tested. Examples of clinical treatment plans were computed, and the results were compared between the two codes. VHEE modality was fully implemented in matRad with GUI capabilities while preserving all original TPS features. New relevant options such as the importation of specific spot-lists or adjustment of the lateral dose calculation cutoff to optimize the calculation speed were validated. Single spot and square field dose distributions were validated in water alone as well as in clinically relevant inhomogeneities. Dose maps from the VHEE model in matRad were in good agreement with TOPAS (2D gamma index [2%/1mm] with passing rates superior to 90%, <6% mean dose differences), except for large interface heterogeneities. This work describes the implementation of a simple but efficient VHEE simulation model in matRad. A few configurations were studied in order to validate the model against accurate Monte Carlo simulations, demonstrating its usefulness for carrying out preliminary studies involving VHEE radiotherapy.

A Highly Efficient and User-Friendly Sensitive Skin Model on the Forearm.

Sensitive skin is a worldwide skin problem, and its assessment of therapeutic efficacy traditionally relies on the facial stinging test. However, this test possesses certain limitations due to its restrictive application site, intense pain sensation, and adverse effects on physical appearance. This study aimed to develop and evaluate a highly efficient and user-friendly sensitive skin simulation model, which combines tape stripping and capsaicin testing on the forearm (FA-TS-CAT), as an alternative to the facial stinging test. A randomized, double-blind, placebo-controlled clinical trial was conducted involving 74 subjects. Skin redness (a* value), transepidermal water loss (TEWL), and self-assessment questionnaires were collected at different time points for analysis. Tape stripping 5 times and 10 min application of capsaicin test were identified as the optimal conditions for the FA-TS-CAT model. Consistent stimulation and natural recovery trends of a* value and TEWL were observed on both the FA-TS-CAT and facial capsaicin test (F-CAT) models within 50 min. After the 4-t-butylcyclohexanol complex emulsion was applied, the a* value in the FA-TS-CAT model exhibited a soothing trend similar to the F-CAT model, with a significantly reduced by 3.99-fold and 3.28-fold at T3 and T4 (p < 0.001), compared to the placebo. Notably, the test efficiency of the FA-TS-CAT model was threefold higher than that of the F-CAT model, and subjects showed more willingness to participate in the FA-TS-CAT test (95.95% vs. 4.05%). These results indicated the FA-TS-CAT is a highly efficient and user-friendly model for sensitive skin, providing a reliable and valid method for clinical research in sensitive skin treatment.

Development of an improved mass transfer model for condensation with dynamic feedback regulation

In the field of condensation research, accurate and efficient numerical simulation models are highly desired. One of the widely used phase change mass transfer models is known as the Lee model. However, this model has limitations due to uncertainties in the mass transfer intensity factor, which can lead to simulation failures and impede large-scale engineering applications. This study presents an improved mass transfer model which employs a tuning function to dynamically and accurately modify the mass transfer intensity factor in each two-phase cell via feedback adjustment. This approach enables immediate and customized adjustment of the factor for each grid within the limit of the tuning function, significantly reducing the errors caused by repeated artificial adjustments and related uncertainties. The adjustment capabilities of the hyperbolic tangent and softsign functions are evaluated. The softsign function is superior in both regulation efficiency and accuracy. The model's accuracy is verified by comparing with previous experiments and simulations, as well as by the one-dimensional Stefan problem. The proposed model achieves high prediction accuracy, reduces the risk of simulation dispersion, and significantly enhances computational efficiency with the iteration number reduced by nearly half under certain conditions compared to the Lee model. Furthermore, the new model shows robustness as the prediction accuracy is insensitive to variations in critical parameters. The improved model is expected to provide valuable assistance for future research and applications in flow condensation with outstanding computational accuracy, efficiency, and stability.

Small modular reactor reinforcement learning framework: Automating reactor core startup

A small modular reactor (SMR) has been considered a potential alternative for achieving carbon neutrality, and therefore, an increasing number of countries are performing extensive research and development. However, this is still in the development stage, and there are several technological or economical challenges that need to be overcome. Minimizing manual operations may be considered a wise approach to reduce the number of operators. Reactor core startup, which is a manual operation, is considered as an example. A method to automate the reactor core startup via the reinforcement learning (RL) algorithm is proposed in this paper. Further, an efficient SMR dynamic simulation model that performs simulations considering the action of the RL agent to achieve states and reward is developed. The suggested SMR dynamic simulation model is validated by the data available in the existing literature. The proposed method can perform automatic reactor core startup. The proposed framework that incorporates the SMR simulator to the RL algorithm is expected to be applied to various cases for reducing manual operations and contributing to realizing a higher level of SMR automation.

Study on the 2D equivalent nonlinear dynamics simulation model related to high speed precision bearing and spindle

The stiffness and contact stress of the bearing spindle system are the key factors affecting its machining accuracy and service life under the condition of high-speed service, which will be affected by different structural parameters and service conditions. It is essential to establish an efficient and accurate computational simulation model to understand the influence of complex factors on the nonlinear dynamic characteristics of the bearing spindle system. Firstly, in the paper, a 2D axisymmetric finite element model of the bearing, aims at the relationship between stiffness and contact stress of the bearing under high-speed service, has been built based on a classical dynamic analysis model and the reversed method of material parameters of equivalent rolling balls. Additionally, for the BT30 spindle, the 2D axisymmetric finite element model of the bearing spindle system also has been built and applied in mechanical analysis of spindle under different conditions of assembly and service, based on the bearing model. The results show that the axial force of bearings decreases as the rotational speed increases, and an augmentation in speed will result in a reduction in the axial stiffness of the BT30 spindle. In addition, the maximum contact stress exhibits a slight decline as the rotational speed increases. Furthermore, with an escalating preload, the stiffness and contact stress of the spindle undergo substantial increments, however, these parameters will cease to alter once a certain threshold is reached.

Research on efficiency simulation model of pumping stations based on data-driven methods

The operational efficiency error of a pumping station unit is affected by several factors, resulting in a large error between the theoretical and actual pumping efficiencies. To solve the problem of accurately simulating the operating efficiency of the pumping station unit, this study conducted research on efficiency simulation models of pumping based on data-driven from three aspects: ①model algorithm, ②feature input and ③response output. In this study, eight machine learning models were introduced to establish pumping unit efficiency simulation models and they were compared with the traditional polynomial regression models, and the models with better performance were selected. Then the experiment proposed using “upstream water level + downstream water level” (UWL + DWL) instead of the traditional “head” (H) as feature input to train the models, and discussed the effects on efficiency simulation accuracy with direct fitting efficiency and fitting power then calculate the efficiency through formula. An example analysis was carried out using the historical data of eight units at Pizhou Station and Suining 2nd Station on the East Line of the South-to-North Water Diversion Project. The experimental results show that ① among all methods, the models based on Gaussian Process Regression (GPR) has the most accurate in ERMS, EMA, R², and EMI indicators, R² is close to 0.92. ②After UWL + DWL was used to train the models, all the test set indicators of the GPR models improved, and the EMA indicator decreased from an average of 0.39–0.26 %. ③ The study found that the fitting efficiency directly is better than the calculation efficiency after fitting the power, but the R² of fitting the power is better than the efficiency, which may provide another idea for the optimal goal of economic operation of pumping stations. ④ On the whole, trainning the GPR models with UWL + DWL to simulate efficiency has the highest precision, for example the EMA and EMI indicators of No.4 unit in Pizhou station can be reduced from 16.49 % and 20.40–0.18 % and 1.55 % respectively. The research results have practical significance and can provide strong support for the economical operation of pump stations.

Electrophysiology lab efficiency using cryoballoon for pulmonary vein isolation in Latin America: A sub-analysis of the Cryo Global Registry Study.

Cryoballoon ablation for pulmonary vein isolation is a time-efficient procedure that can alleviate stress on electrophysiology lab resources. This analysis modeled the impact of cryoballoon ablation on electrophysiology lab operation using data from Latin America. Data from centers in Argentina, Mexico, Colombia, and Chile of the were used as inputs for an electrophysiology lab efficiency simulation model. The model used the assumption that either two (today's electrophysiology lab operations) or three (including electrophysiology lab operational changes) cryoballoon ablation procedures could be performed per day. The endpoints were the percentage of days that resulted in 1) overtime and 2) time left for an extra non-ablation electrophysiology procedure. Data from a total of 232 procedures from six Latin American centers were included in the analysis. The average electrophysiology lab occupancy time for all procedures in Latin America was 132 ± 62 minutes. In the Current Scenario (two procedures per day), 7.4% of simulated days resulted in overtime, and 81.4% had enough time for an extra electrophysiology procedure. In the Enhanced Productivity Scenario (three procedures per day), 16.4% of days used overtime, while 67.4% allowed time for an extra non-ablation electrophysiology procedure. Using real-world, Latin American-specific data, we found that with operational changes, three ablation procedures could feasibly be performed daily, leaving time for an extra electrophysiology procedure on more than half of days. Thus, use of cryoballoon ablation is an effective tool to enhance electrophysiology lab efficiency in resource-constrained regions such as Latin America.

Experimental validation of an inverse method for defect reconstruction in a two-dimensional waveguide model.

Defect reconstruction is essential in non-destructive testing and structural health monitoring with guided ultrasonic waves. This paper presents an algorithm for reconstructing notches in steel plates, which can be seen as artificial defects representing cracks by comparing measured results with those from a simulation model. The model contains a parameterized notch, and its geometrical parameters are to be reconstructed. While the algorithm is formulated and presented in a general notation, a special case of guided wave propagation is used to investigate one of the simplest possible simulation models that discretizes only the cross section of the steel plate. An efficient simulation model of the plate cross section is obtained by the semi-analytical scaled boundary finite element method. The reconstruction algorithm applied is gradient-based, and algorithmic differentiation calculates the gradient. The dedicated experimental setup excites nearly plane wave fronts propagating orthogonal to the notch. A scanning laser Doppler vibrometer records the velocity field at certain points on the plate surface as input to the reconstruction algorithm. Using two plates with notches of different depths, it is demonstrated that accurate geometry reconstruction is possible.

Understanding the xenon primary scintillation yield for cutting-edge rare event experiments

Xenon scintillation has been widely used in rare event detection experiments, such as in neutrinoless double beta decay, double electron captures and dark matter searches. Nonetheless, experimental values for primary scintillation yield in gaseous xenon (GXe) remain scarce and dispersed. The mean energy required to produce a scintillation photon, w sc, in GXe in the absence of recombination has been measured to be in the range of 34–111 eV. Lower w sc-values were reported for α-particles when compared to electrons produced by γ- or x-rays. Since w sc is expected to be similar for x-, γ-rays or electrons and almost equal to that obtained for α-particles, the above difference can not be understood. In addition, at present one may also pose the question of a dependence of w sc on photon energy. We carried out a systematic study on the absolute primary scintillation yield in GXe under reduced electric fields in the 70–300 V cm-1 bar-1 range and near atmospheric pressure, 1.2 bar, supported by a robust geometrical efficiency simulation model. We were able to clear-out the above standing problems: w sc was determined for x/γ-rays in the 5.9–60 keV energy range as well as for α-particles in the 1.5–2.5 MeV range, and no significant dependency neither on radiation type nor on energy has been observed. Our experimental w sc-values agree well with both up-to-date simulations and literature data obtained for α-particles. The discrepancy between our results and the experimental values found in the literature for x/γ-rays is discussed in this work and attributed to unaddressed large systematic errors in those previous studies. These findings can be extrapolated to other gases, and have impact on experiments such as double beta decay, double electron capture and directional dark matter searches while also on potential future detection systems such as DUNE-Gas. Only assuming the VUV emission band as is the case of most of the literature values, a mean w sc-value of 38.7 ± 0.6 (sta.)+7.7 -7.2 (sys.) eV was obtained. If the UV-VIS emission band is to be considered, the average energy to produce a photon was determined to be w 2nd = 43.5 ± 0.7 (sta.)+8.7 -8.1 (sys.) eV and w 3rd = 483 ± 7 (sta.+110 -105 (sys.) eV, in the VUV and UV-VIS bands, respectively.

Enhanced forming height and accuracy of thin-walled aluminum alloy by impact pneumatic forming

To enhance the plastic deformation capacity of hard-to-deform metal materials, the utilization of impact pneumatic forming technology is proposed for shaping complex thin-walled structures within milliseconds at room temperature. In this study, an efficient numerical simulation model is established and experiments were performed to investigate the forming height, limits, and accuracy of aluminum alloy components. The experimental results show a 21.4 % increase in the ultimate forming height when employing impact pneumatic forming as compared to quasi-static pneumatic forming. Moreover, as the initial gas pressure increases, part forming height experiences an increase but the gas compression rate experiences a decline. The simulation results reveal a maximum deformation velocity of 43.19 m/s and a limited strain rate exceeding 134 s−1, affirming the connection between increased forming height and high strain rate. Furthermore, the actual contours of parts under different gas pressures align with the simulation results, validating the reliability of the simulation. It is shown that a high gas pressure of more than 20 MPa applied for a long time can improve the forming accuracy of flat bottom and wave parts. Microstructural analysis shows that dislocations in the specimens subjected to IPF conditions are better distributed, and the dimples at the fracture sites are more pronounced. This further substantiates that the IPF process improves the plastic deformation capacity of hard-to-deform materials.

Accurate and Efficient Simulation Models for Power Electronics Transformers Based on Series-Connected Active Unity Power Factor Rectifier Modules

This paper contributes an efficient simulation technique for input-series output-parallel multilevel power electronics transformers based on active unity-power-factor rectifiers as building blocks. The technical motivation of the work comes from the fact that the computational burden for the simulation of these technologies tends to become unaffordable as the number of modules grows when using commercial software blocksets. This paper presents a new method to drastically reduce the simulation complexity by simplifying the switching rules: in a three-phase circuit, each phase zero-crossing condition is implemented by a single and simple algebraic rule, so the complex calculations for determining the conduction state of each single diode are removed from the model. The computational enhancement and accuracy of the proposed technique are proved by experimental verification using a single-phase single-cell prototype together with multiple simulations of full-scale systems of different sizes.

Modelling of sap flux density of oak in a humid region in China

AbstractTranspiration plays a vital role in determining the watershed water cycle. However, we still have little knowledge of the characteristics of tree transpiration in the Hanjiang River Basin, which is the water source for the middle route of South‐to‐North water diversion project. Here, we measured sap flux density of oak trees (Quercus, the dominant species here) at the 10‐min resolution for 2 years and explored its response to the environmental conditions. The incoming short‐wave radiation and vapour pressure deficit well explained the variation of daytime sap flux density, and a statistical model was then proposed to calculate the daytime sap flux density correspondingly; then a nighttime sap flux density module was proposed based on the daytime sap flux density calculation. Sap flux density showed clear counter‐clockwise hysteresis response to incoming short‐wave radiation, and clockwise hysteresis response to vapour pressure deficit. Our sap flux density model can well reproduce the corresponding hysteresis response to incoming short‐wave radiation and vapour pressure deficit. This study unravelled the environmental controls of sap flux density of the oak trees in the Hanjiang River Basin, proposed an efficient model for the sap flux density simulation, provided important knowledge for understanding the corresponding forests' water use, which is of critical significance in determining the water availability for the middle route of the South‐to‐North water diversion project.

Patterns of Nanoporous Spherical Packing Emerging under Influence of Curvature and Confinement

Nanoporous membranes are popular in nanotechnology due to biomedical and industrial applications. During the past decade, experimental, theoretical and computational research into porous membranes and soft materials has opened up new mathematical dimensions. In bulk, diblock copolymers exhibit ordered morphologies such as parallel matrices of lamellae, bicontinuous matrices of gyroids, hexagonal matrices of cylinders and body-centred cubic matrices of spheres. In melt, confinement plays an essential role in tuning the frustration of the diblock copolymer system to predict more nanostructures. These nanostructures depend on the composition of the copolymers, their confining geometries and the degree of structural frustration. An isotropic 9-point stencil for Laplacian is constructed. The discrete finite-difference technique is used in polar grids to discretize the macromolecule of the diblock copolymer system to study spherical patterns to study the effect of curvature and confinement with a well-known and efficient cell dynamic simulation model. Intel FORTRAN (IFORT) codes are generated to run the CDS model and visualisation of simulation results is observed with the help of OPENDX. A comparison of the proposed study with existing experimental and computational studies is also presented.

Determining appropriate level of detail of 3D aggregate model for accurate and efficient mesoscopic simulation of asphalt concrete

The levels of detail (LODs) of aggregate models significantly impact both the accuracy and efficiency of the mesoscale numerical simulation of asphalt concrete. This study proposed a quantitative evaluation framework to find an appropriate LOD that allows accurate simulation of asphalt concrete with relatively low model complexity. First, the coarse aggregates in asphalt concrete were reconstructed from computed tomography (CT) images, and their LOD was defined as level-0. Each reconstructed aggregate was then simplified using a surface simplification method that obtains aggregate models with four descending LODs (levels-1, 2, 3 and 4), consisting of 200, 100, 50 and 20 triangular facets respectively. The simulation accuracy was evaluated according to several aggregate geometric indexes and mesoscopic finite element (FE) compressive simulation results of asphalt concrete. The results indicate that compared to the level-1 model, the level-2 model can achieve a similar simulation accuracy with a 50% reduction in simulation time.

A reactive molecular dynamics model for uranium/hydrogen containing systems.

Uranium-based materials are valuable assets in the energy, medical, and military industries. However, understanding their sensitivity to hydrogen embrittlement is particularly challenging due to the toxicity of uranium and the computationally expensive nature of quantum-based methods generally required to study such processes. In this regard, we have developed a Chebyshev Interaction Model for Efficient Simulation (ChIMES) that can be employed to compute energies and forces of U and UH3 bulk structures with vacancies and hydrogen interstitials with accuracy similar to that of Density Functional Theory (DFT) while yielding linear scaling and orders of magnitude improvement in computational efficiency. We show that the bulk structural parameters, uranium and hydrogen vacancy formation energies, and diffusion barriers predicted by the ChIMES potential are in strong agreement with the reference DFT data. We then use ChIMES to conduct molecular dynamics simulations of the temperature-dependent diffusion of a hydrogen interstitial and determine the corresponding diffusion activation energy. Our model has particular significance in studies of actinides and other high-Z materials, where there is a strong need for computationally efficient methods to bridge length and time scales between experiments and quantum theory.

Efficient 2D Neck Model for Simulation of the Whiplash Injury Mechanism.

Whiplash injuries, mainly located in the neck, are one of the most common injuries resulting from road collisions. These injuries can be particularly challenging to detect, compromising the ability to monitor patients adequately. This work presents the development and validation of a computationally efficient model, called Efficient Neck Model-2D (ENM-2D), capable of simulating the whiplash injury mechanism. ENM-2D is a planar multibody model consisting of several bodies that model the head and neck with the same mass and inertia properties of a male occupant model in the 50th percentile. The damping and non-linear spring parameters of the kinematic joints were identified through a multiobjective optimization process, solved sequentially. The TNO-Human Body Model (TNO-HBM), a validated occupant model for rear impact, was simulated, and its responses were used as a reference for validation purposes. The root mean square (RMS) of the deviations of angular positions of the bodies were used as objective functions, starting from the bottom vertebra to the top, and ending in the head. The sequence was repeated until it converged, ending the optimization process. The identified ENM-2D model could simulate the whiplash injury mechanism kinematics and accurately determine the injury criteria associated with head and neck injuries. It had a relative deviation of 8.3% for the head injury criteria and was 12.5 times faster than the reference model.

Efficient hydraulic and thermal simulation model of the multi-phase natural gas production system with variable speed compressors

The natural gas production system is a very complex system, involving pipelines, compressors and valves with different structures and calculation parameters. It can be divided into two different parts: gas production and collection pipe networks. Fluid flow in the gas production pipe network is multi-phase flow. Fluid flow in the gas collection pipe network is single-phase flow. It is imperative to consider gas production and collection pipe networks in conjunction to ensure accurate operation simulation. The complexity of the network structures and flow statuses can cause computational instability or even divergence problems in simulations when coupling these two types of pipe networks. To address this issue, an automatic and practical node numbering method is proposed for the large-scale pipe network, which can ensure the full rank of the solution matrix and computational stability. On the other hand, due to the need for frequent adjustments of the pipe networks to satisfy the production demand, computational boundary treatments of constant inlet/outlet pressure, constant flow rate or constant pressure ratio for the compressor stations are not suitable. To address this issue, the characteristic curves of compressors are coupled into the simulation of pipe networks to represent the variable-speed centrifugal and reciprocating compressors.The accuracy and robustness of the proposed models and numerical methods are validated through comparisons with software results and field data. The simulation time is only within 0.5 s for the natural gas production system with 210 nodes and 176 pipelines. Our model has relative deviations within 3% in both pressure and flow rate compared to field data and within 10% compared to software.

An Efficient Half-Bridge MMC Model for EMTP-Type Simulation Based on Hybrid Numerical Integration

Electromagnetic transient (EMT) simulation is critical and fundamental in the design and operation of the modular multilevel converter (MMC). This paper proposes a highly efficient EMT simulation model for MMC based on hybrid numerical integration. The topology and operational principle of MMC are elaborated first. Based on this, an efficient simulation model for MMC is proposed. Each arm of the MMC is reduced to a two-node Norton equivalent circuit in the main network simulation. The computation of the capacitor dynamic equations is decoupled from that of the arm inductor dynamic equation. They are computed in a leapfrog manner. This makes the equivalent conductance of the MMC arm constant and greatly improves the simulation efficiency. Moreover, the dynamic equations of the capacitors are also decoupled from each other. Various operational conditions of the MMC are also considered, and accuracy and adaptability are thus ensured. Extensive studies on power systems with different scales verify the accuracy and improved efficiency of the proposed EMT simulation model for MMC.

Morphological Investigation of Lamellae Patterns in Diblock Copolymers under Change of Thickness and Confinement in Polar Geometry

Mathematicians collaborate computationally with practical scientists to predict the novel morphologies soft materials, having potential applications in nanotechnology. This work presents the novel lamellae morphology that the confined diblock copolymer system displayed inside the polar geometry in order to achieve this, cell dynamics simulations (CDS) model is employed on a polar mesh to study the special impacts of confinement on the self-assembly behavior of diblock copolymer systems. Under the numerical formulation of the isotropic Laplacian with polar geometry employed in the CDS model, the set of 9-point stencil is considered to discretize the Laplacian operator on polar mesh system. FTCS finite difference mechanism is taken into consideration for discretization of Laplacian operator due to its computational efficiency and accuracy. Cell dynamics simulation is efficient simulation model for large-scale simulation as compared to the other models available in literature. In the simulation, evolutionary lamella morphology is presented with and without confinement for various sizes of the circular annular pores. A comparative review of lamella morphologies achieved by simulation in comparison of experimental study is presented, coupled with a thorough investigation of symmetric and asymmetric morphologies in captivity.

Verification of an open-source Python library for the simulation of district heating networks with complex topologies

District Heating Networks are seen as a popular solution for the decarbonation of space and domestic hot water heating by the use of renewables or waste heat. Their design and operation can be enhanced both environmentally and economically through the use of dedicated simulation tools.This work presents a new multicomponent Python-based software library including an efficient steady-state model for the hydraulic simulation and a Lagrange-based dynamic model for the thermal part. The model is verified on real data from a meshed DHN with a granularity of 15 min. For the considered period of 6 days, the model estimated the return temperatures of two heat plants with a mean error of 0.08 K and 0.43 K and standard deviations of 0.56 K and 0.71 K respectively. On the hydraulic part, after applying a fixed correction factor, the error on the pressure differences was estimated in 3 peripheral locations of the network. In the worst case, the relative error distribution had a mean of 0.38% and a standard deviation of 8.74%. Finally, the implemented hydraulic solver achieved a speed improvement over the standard loop method of 17.5%.