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Numerical simulation of the single point incremental forming (SPIF) processes can be very demanding and time consuming due to the constantly changing contact conditions between the tool and the sheet surface, as well as the nonlinear material behaviour combined with non-monotonic strain paths. The purpose of this paper is to propose an adaptive remeshing technique implemented in the in-house implicit finite element code LAGAMINE, to reduce the simulation time. This remeshing technique automatically refines only a portion of the sheet mesh in vicinity of the tool, therefore following the tool motion. As a result, refined meshes are avoided and consequently the total CPU time can be drastically reduced.

SPIF is a dieless manufacturing process in which a sheet is deformed by using a tool with a spherical tip. This dieless feature makes the process appropriate for rapid-prototyping and allows for an innovative possibility to reduce overall costs for small batches, since the process can be performed in a rapid and economic way without expensive tooling. As a consequence, research interest related to SPIF process has been growing over the last years.

In this work, the proposed automatic refinement technique is applied within a reduced enhanced solid-shell framework to further improve numerical efficiency. In this sense, the use of a hexahedral finite element allows the possibility to use general 3D constitutive laws. Additionally, a direct consideration of thickness variations, double-sided contact conditions and evaluation of all components of the stress field are available with solid-shell and not with shell elements. Additionally, validations by means of benchmarks are carried out, with comparisons against experimental results.

It is worth noting that no previous work has been carried out using remeshing strategies combined with hexahedral elements in order to improve the computational efficiency resorting to an implicit scheme, which makes this work innovative. Finally, it has been shown that it is possible to perform accurate and efficient finite element simulations of SPIF process, resorting to implicit analysis and continuum elements. This is definitively a step-forward on the state-of-art in this field.

This paper aims to present an approach for the numerical simulation of concrete shrinkage. First, some physical mechanisms of shrinkage are described and then the developed numerical model for the analysis of shrinkage of spatial three-dimensional structures using thermal analogy is presented. Results of the real behavior of structures because of concrete shrinkage using the developed numerical model are compared with the experimental and it is clearly shown that the developed numerical model is an efficient tool in predicting the time-dependent behavior of all concrete structures.

In this paper, Fib Model Code 2010 to predict shrinkage deformation of concrete is used, and it was incorporated in the three-dimensional numerical model using the thermal analogy. Mentioned three-dimensional numerical model uses the modified Rankine material law to describe concrete behavior in tension and modified Mohr-Coulomb material law to describe concrete behavior in compression. The developed three-dimensional numerical model successfully analyzes the behavior of reinforced and/or prestressed concrete structures including time-dependent deformations of concrete as well.

Results are shown in this paper clearly demonstrate the reliability of the developed numerical model in predicting the shrinkage strain, as well as its impact on concrete and reinforced concrete structures. The results obtained using the developed numerical model are in better agreement with the experimental results, than the results obtained using the numerical models from literature that also use the Fib Model Code 2010 to predict the shrinkage strain. So, it can be concluded that for a real simulation of concrete structures, alongside the model for predicting the shrinkage strain, the models for concrete behavior in tension and compression have a very important role.

Results of the developed three-dimensional numerical model were compared with experimental results from literature and with theoretical foundations, and it can be talked that this numerical model presents a good tool for analysis of reinforced and prestressed concrete structures including shrinkage deformation of concrete. Results obtained using the developed three-dimensional numerical model are better agreed with experimental than results of other numerical model from literature.

Using appropriate solution techniques for transformer inrush current transient study is of great prominence owing to the inevitable inclusion of differential equations leading to complicated analysis procedures. This study aims to propose an analytical-numerical method to accurately analyze the three-phase three-limb core-type transformer inrush current in different cases considering the nonlinear behavior of the iron core.

The proposed method focuses on acquiring equations for inrush current and also the magnetic core flux by the application of a simulation-based iterative approach. In this regard, multiple integral equations are solved taking the time intervals into account. Then several derivations and integrations of matrix terms are substituted into the obtained results so as to simplify the solution process.

The method provides notable enhancements in computation time and also excellent qualities of accuracy compared with conventional numerical methods.

The proposed method is simulated for two three-phase transformers via MATLAB software. The obtained simulation results have been also compared with experimental tests.

Actually, the analytical-numerical method is capable of computing higher number of iterations in a shorter time efficiently, while making use of the conventional numerical procedures may not result in expected convergences. The simulation results of the proposed analytical-numerical technique illustrate a close agreement with the experimental test, and hence, verify the method preciousness.

Experimental results play a crucial role in the validation of mathematical and numerical models for a variety of basic and applied thermal transport problems. The purpose of this paper is to focus on the role played by experimentation in an accurate numerical simulation of thermal processes and systems.

The paper takes the form of a numerical simulation combined with experimentation. The paper presents various circumstances where the numerical simulation may be efficiently combined with experimentation, and indeed driven by experimental data, to obtain accurate, valid and realistic numerical predictions.

The paper demonstrates validation and accuracy of numerical simulation.

This paper is an important first step in combining experiments and simulation for complex thermal systems.

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.

The purpose of this study is to analyze the influence of the main physical–numerical parameters in the computational evaluation of natural convection heat transfer rates in isothermal flat square plates in the laminar regime. Moreover by experimentally validate the results of the numerical models and define the best parameter settings for the problem situation studied.

The present work is an extension of the study by Verderio Junior et al. (2021), differing in the modeling, results analysis and conclusions for the laminar flow regime with Rade=1×105. The analysis of the influence and precision of the physical–numerical parameters: boundary conditions, degree of mesh refinement, refinement layers and κ – ω SST and κ – ε turbulence models, occurred from the results from 48 numerical models, which were simulated using the OpenFOAM® software. Comparing the experimental mean Nusselt number with the numerical values obtained in the simulations and the analysis of the relative errors were used in the evaluation of the advantages, restrictions and selection of the most adequate parameters to the studied problem situation.

The numerical results of the simulations were validated, with excellent precision, from the experimental reference by Kitamura et al. (2015). The application of the κ – ω SST and κ – ε turbulence models and the boundary conditions (with and without wall functions) were also physically validated. The use of the κ – ω SST and κ – ε turbulence models, in terms of cost-benefit and precision, proved to be inefficient in the problem situation studied. Simulations without turbulence models proved to be the best option for the physical model for the studies developed. The use of refinement layers, especially in applications with wall functions and turbulence models, proved unfeasible.

Use of the physical–numerical parameters studied and validated, and application of the modeling and analysis methodology developed in projects and optimizations of natural convection thermal systems in a laminar flow regime. Just like, reduce costs and the dependence on the construction of experimental apparatus to obtain experimental results and in the numerical-experimental validation process.

Exclusive use of free and open-source computational tools as an alternative to feasible research in the computational fluid dynamics area in conditions of budget constraints and lack of higher value-added infrastructure, with applicability in the academic and industrial areas.

The results and discussions presented are original and new for the applied study of laminar natural convection in isothermal flat plate, with analysis and validation of the main physical and numerical influence parameters.

The purpose of this paper is to present outcomes of efforts made over the last 20 years to extend the applicability of the Richardson extrapolation procedure to numerical predictions of multidimensional, steady and unsteady, fluid flow and heat transfer phenomena in regular and irregular calculation domains.

Pattern-preserving grid-refinement strategies are proposed for mathematically rigorous generalizations of the Richardson extrapolation procedure for numerical predictions of steady fluid flow and heat transfer, using finite volume methods and structured multidimensional Cartesian grids; and control-volume finite element methods and unstructured two-dimensional planar grids, consisting of three-node triangular elements. Mathematically sound extrapolation procedures are also proposed for numerical solutions of unsteady and boundary-layer-type problems. The applicability of such procedures to numerical solutions of problems with curved boundaries and internal interfaces, and also those based on unstructured grids of general quadrilateral, tetrahedral, or hexahedral elements, is discussed.

Applications to three demonstration problems, with discretizations in the asymptotic regime, showed the following: the apparent orders of accuracy were the same as those of the numerical methods used; and the extrapolated results, measures of error, and a grid convergence index, could be obtained in a smooth and non-oscillatory manner.

Strict or approximate pattern-preserving grid-refinement strategies are used to propose generalized Richardson extrapolation procedures for estimating grid-independent numerical solutions. Such extrapolation procedures play an indispensable role in the verification and validation techniques that are employed to assess the accuracy of numerical predictions which are used for designing, optimizing, virtual prototyping, and certification of thermofluid systems.

The purpose of this study is to investigate the aerosol dynamics of the particle coagulation process using a newly developed weighted fraction Monte Carlo (WFMC) method.

The weighted numerical particles are adopted in a similar manner to the multi-Monte Carlo (MMC) method, with the addition of a new fraction function (α). Probabilistic removal is also introduced to maintain a constant number scheme.

Three typical cases with constant kernel, free-molecular coagulation kernel and different initial distributions for particle coagulation are simulated and validated. The results show an excellent agreement between the Monte Carlo (MC) method and the corresponding analytical solutions or sectional method results. Further numerical results show that the critical stochastic error in the newly proposed WFMC method is significantly reduced when compared with the traditional MMC method for higher-order moments with only a slight increase in computational cost. The particle size distribution is also found to extend for the larger size regime with the WFMC method, which is traditionally insufficient in the classical direct simulation MC and MMC methods. The effects of different fraction functions on the weight function are also investigated.

Stochastic error is inevitable in MC simulations of aerosol dynamics. To minimize this critical stochastic error, many algorithms, such as MMC method, have been proposed. However, the weight of the numerical particles is not adjustable. This newly developed algorithm with an adjustable weight of the numerical particles can provide improved stochastic error reduction.

In many scientific and engineering fields, large‐scale heat transfer problems with temperature‐dependent pore‐fluid densities are commonly encountered. For example, heat transfer from the mantle into the upper crust of the Earth is a typical problem of them. The main purpose of this paper is to develop and present a new combined methodology to solve large‐scale heat transfer problems with temperature‐dependent pore‐fluid densities in the lithosphere and crust scales.

The theoretical approach is used to determine the thickness and the related thermal boundary conditions of the continental crust on the lithospheric scale, so that some important information can be provided accurately for establishing a numerical model of the crustal scale. The numerical approach is then used to simulate the detailed structures and complicated geometries of the continental crust on the crustal scale. The main advantage in using the proposed combination method of the theoretical and numerical approaches is that if the thermal distribution in the crust is of the primary interest, the use of a reasonable numerical model on the crustal scale can result in a significant reduction in computer efforts.

From the ore body formation and mineralization points of view, the present analytical and numerical solutions have demonstrated that the conductive‐and‐advective lithosphere with variable pore‐fluid density is the most favorite lithosphere because it may result in the thinnest lithosphere so that the temperature at the near surface of the crust can be hot enough to generate the shallow ore deposits there. The upward throughflow (i.e. mantle mass flux) can have a significant effect on the thermal structure within the lithosphere. In addition, the emplacement of hot materials from the mantle may further reduce the thickness of the lithosphere.

The present analytical solutions can be used to: validate numerical methods for solving large‐scale heat transfer problems; provide correct thermal boundary conditions for numerically solving ore body formation and mineralization problems on the crustal scale; and investigate the fundamental issues related to thermal distributions within the lithosphere. The proposed finite element analysis can be effectively used to consider the geometrical and material complexities of large‐scale heat transfer problems with temperature‐dependent fluid densities.

While still arguing whether a quasi‐linear equation has a “stability” problem in integration, comparative analyses are made by numerical experimentations using conservation with smoothing and non‐conservation schemes as well as a time‐moving treatment scheme proposed by the first author respectively. The results show that the solution seeking method of the quasi‐linear model should not be considered as a “stability” problem. The traditional well‐posed computational model needs to be improved. The Lorenz’s “butterfly effect” should be in nature a Richardson’s explosive increase in time evolution of moving fluid.