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Presents three non‐isothermal, time dependent, three dimensional examples having cylindrical geometries to show the significant effort of numerical precision and dissipation on rotating flow predictions. The examples are relevant to turbomachinery design and geophysical studies. Discusses the relationship between numerical precision, numerical dissipation and co‐ordinate system angular velocity. Compares predictions made in stationary and rotating co‐ordinate systems, using contour plots of dimensionless stream function and temperature. Shows that wrong, axisymmetric solutions are predicted if the co‐ordinate system is not selected to minimize relative tangential velocities/Peclet numbers, thereby increasing numerical precision and reducing dissipation.

This paper aims to study, experimentally validate and select the main physical and numerical parameters of influence in computational numerical simulations to evaluate mean heat flux by natural convection on square flat plates.

Several numerical models were built to study the influence of physical and numerical parameters about the predictions of the natural convection heat transfer rates on the surface of a flat plate with aspect ratio = 1, in isothermal conditions, turbulent regime and using the free and open-source software OpenFOAM®. The studied parameters were: boundary conditions (using or not using wall functions in properties ε, κ, ν_t and ω), degree of mesh refinement, refinement layers and turbulence models [κ – ε and κ – ω Shear Stress Transport (SST)]. From the comparison of the values of the mean Nusselt number, obtained from numerical simulations and literature experimental results, the authors evaluated the precision of the studied parameters, validating and selecting the most appropriate to the analyzed problem situation.

The validation and agreement of the numerical results could be proven with excellent precision from experimental references of the technical scientific literature. More refined meshes with refinement layers were not suitable for the studies developed. The κ – ε and κ – ω SST turbulence models, in meshes without refinement layers, proved to be equivalent. Whether or not to use wall functions in turbulent boundary conditions proved to be irrelevant as to the accuracy of results for the problem situation studied.

Use of the physical and numerical parameters is studied and validated for various applications in natural convection heat transfer of technology and industry areas.

Use of free and open-source software as a research tool in the Computational Fluid Dynamics (CFD) area, especially in conditions without large financial resources or state-of-the-art infrastructure.

To the best of the authors’ knowledge, this work is yet not available in existing literature.

Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography at the end contains 2,177 references to papers, conference proceedings and theses/dissertations dealing with the subjects that were published in 1990‐2000.

Reviews briefly the history of management games and outlines the main parts of a game. Lists the best known international management games being utilized in the United States. Provides a complete description of the Multinational Management Game (MMG) along with case histories of management development experiences with MMG in Korea, the Pacific Asian Management Programme, The University of Hawaii, The Japan American Institute of Management Science, a programme in Hungary, and an Executive MBA Programme in the United States. Includes excerpts from student experiences within game play and a short review of research validating games as learning environments.

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.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

This paper aims to propose an efficient and convenient numerical algorithm for two-dimensional nonlinear Volterra-Fredholm integral equations and fractional integro-differential equations (of Hammerstein and mixed types).

The main idea of the presented algorithm is to combine Bernoulli polynomials approximation with Caputo fractional derivative and numerical integral transformation to reduce the studied two-dimensional nonlinear Volterra-Fredholm integral equations and fractional integro-differential equations to easily solved algebraic equations.

Without considering the integral operational matrix, this algorithm will adopt straightforward discrete data integral transformation, which can do good work to less computation and high precision. Besides, combining the convenient fractional differential operator of Bernoulli basis polynomials with the least-squares method, numerical solutions of the studied equations can be obtained quickly. Illustrative examples are given to show that the proposed technique has better precision than other numerical methods.

The proposed algorithm is efficient for the considered two-dimensional nonlinear Volterra-Fredholm integral equations and fractional integro-differential equations. As its convenience, the computation of numerical solutions is time-saving and more accurate.

This study aims to overcome the involved challenging issues and provide high-precision eigensolutions. General eigenproblems in the system of ordinary differential equations (ODEs) serve as mathematical models for vector Sturm-Liouville (SL) and free vibration problems. High-precision eigenvalue and eigenfunction solutions are crucial bases for the reliable dynamic analysis of structures. However, solutions that meet the error tolerances specified are difficult to obtain for issues such as coefficients of variable matrices, coincident and adjacent approximate eigenvalues, continuous orders of eigenpairs and varying boundary conditions.

This study presents an h-version adaptive finite element method based on the superconvergent patch recovery displacement method for eigenproblems in system of second-order ODEs. The high-order shape function interpolation technique is further introduced to acquire superconvergent solution of eigenfunction, and superconvergent solution of eigenvalue is obtained by computing the Rayleigh quotient. Superconvergent solution of eigenfunction is used to estimate the error of finite element solution in the energy norm. The mesh is then, subdivided to generate an improved mesh, based on the error.

Representative eigenproblems examples, containing typical vector SL and free vibration of beams problems involved the aforementioned challenging issues, are selected to evaluate the accuracy and reliability of the proposed method. Non-uniform refined meshes are established to suit eigenfunctions change, and numerical solutions satisfy the pre-specified error tolerance.

The proposed combination of methodologies described in the paper, leads to a powerful h-version mesh refinement algorithm for eigenproblems in system of second-order ODEs, that can be extended to other classes of applications in damage detection of multiple cracks in structures based on the high-precision eigensolutions.

The purpose of this paper is to evaluate some numerical integration strategies used in generalized (G)/extended finite element method (XFEM) to solve linear elastic fracture mechanics problems. A range of parameters are here analyzed, evidencing how the numerical integration error and the computational efficiency are improved when particularities from these examples are properly considered.

Numerical integration strategies were implemented in an existing computational environment that provides a finite element method and G/XFEM tools. The main parameters of the analysis are considered and the performance using such strategies is compared with standard integration results.

Known numerical integration strategies suitable for fracture mechanics analysis are studied and implemented. Results from different crack configurations are presented and discussed, highlighting the necessity of alternative integration techniques for problems with singularities and/or discontinuities.

This study presents a variety of fracture mechanics examples solved by G/XFEM in which the use of standard numerical integration with Gauss quadratures results in loss of precision. It is discussed the behaviour of subdivision of elements and mapping of integration points strategies for a range of meshes and cracks geometries, also featuring distorted elements and how they affect strain energy and stress intensity factors evaluation for both strategies.

The paper gives the description of boundary element method (BEM) with subdomains for the solution of convection—diffusion equations with variable coefficients and Burgers’ equations. At first, the whole domain is discretized into K subdomains, in which linearization of equations by representing convective velocity by the sum of constant and variable parts is carried out. Then using fundamental solutions for convection—diffusion linear equations for each subdomain the boundary integral equation (in which the part of the convective term with the constant convective velocity is not included into the pseudo‐body force) is formulated. Only part of the convective term with the variable velocity, which is, as a rule, more than one order less than convective velocity constant part contribution, is left as the pseudo‐source. On the one hand, this does not disturb the numerical BEM—algorithm stability and, on the other hand, this leads to significant improvement in the accuracy of solution. The global matrix, similar to the case of finite element method, has block band structure whereas its width depends only on the numeration order of nodes and subdomains. It is noted, that in comparison with the direct boundary element method the number of global matrix non‐zero elements is not proportional to the square of the number of nodes, but only to the total number of nodal points. This allows us to use the BEM for the solution of problems with very fine space discretization. The proposed BEM with subdomains technique has been used for the numerical solution of one‐dimensional linear steady‐state convective—diffusion problem with variable coefficients and one‐dimensional non‐linear Burgers’ equation for which exact analytical solutions are available. It made it possible to find out the BEM correctness according to both time and space. High precision of the numerical method is noted. The good point of the BEM is the high iteration convergence, which is disturbed neither by high Reynolds numbers nor by the presence of negative velocity zones.