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The purpose of this paper is to first present the key features of hybrid numerical methods that enable cost-effective simulations of complex thermofluid systems, and then demonstrate the formulation and application of such a method.

A hybrid numerical method is formulated for simulations of a closed-loop thermosyphon operating with slurries of a micro-encapsulated phase-change material suspended in distilled water. The slurries are modeled as homogeneous mixtures, with inputs of effective properties and overall heat-loss coefficients. Combinations of an axisymmetric two-dimensional (2D) control-volume finite-element method and a segmented-quasi-one-dimensional (1D) model are used to achieve cost-effective simulations. Proper matching of the solutions at the interfaces between adjacent axisymmetric 2D and quasi-1D zones is ensured by incorporating and heuristically determining suitable lengths of pre- and post-heating (and also pre- and post-cooling) sections.

In the demonstration problem, which would strictly require full three-dimensional simulations of the fluid flow and heat transfer phenomena, the proposed hybrid 1D/2D numerical method produces results that are in very good agreement with those obtained in a complementary experimental investigation.

The hybrid numerical methods discussed in this paper allow cost-effective computer simulations of complex thermofluid systems. These methods can therefore serve as very useful tools for the design, parametric studies, and optimization of such systems.

This paper employs a hybrid numerical method combining the differential transformation method (DTM) and the finite difference method (FDM) to study the bifurcation and nonlinear behavior of a rigid rotor supported by a relative short gas lubricated journal bearing system with herringbone grooves. The analysis reveals a complex dynamic behavior comprising periodic, subharmonic and quasi‐periodic responses of the rotor center. The dynamic behavior of the bearing system varies with changes in the rotor mass and bearing number. The current analytical results are found to be in good agreement with those of other numerical methods. This paper discusses these issues.

In this paper, DT is used to deal Reynolds equation and is also one of the most widely used techniques for solving differential equations due to its rapid convergence rate and minimal calculation error. A further advantage of this method over the integral transformation approach is its ability to solve nonlinear differential equations. In solving the Reynolds equation for the current gas bearing system, DTM is used for taking transformation with respect to the time domain τ, and then the FDM is adopted to discretize with respect to the directions of coordinates.

From the Poincaré maps of the rotor center as calculated by the DTM&FDM method with different values of the time step, it can be seen that the rotor center orbits are in agreement to approximately four decimal places for the different time steps. The numerical studies also compare the results obtained by the SOR&FDM and DTM&FDM methods for the orbits of the rotor center. It is observed that the results calculated by DTM&FDM are more accurately than SOR&FDM. Therefore, the DTM&FDM method suits this gas bearing system and provides better convergence than SOR&FDM method.

This study utilizes a hybrid numerical scheme comprising the DTM and the FDM to analyze nonlinear dynamic behavior of a relative short gas lubricated journal bearing system with herringbone grooves. The system state trajectory, phase portraits, the Poincaré maps, the power spectra, and the bifurcation diagrams reveal the presence of a complex dynamic behavior comprising periodic, subharmonic and quasi‐periodic responses of the rotor center. Therefore, the proposed method provides an effective means of gaining insights into the nonlinear dynamics of relative short gas lubricated journal bearing systems with herringbone grooves.

Hybrid methods, wherefore numerical and experimental data are used to calculate a critical parameter, have been used for several years with great success in Experimental Mechanics and, in particular, in fracture mechanics. The purpose of this paper is to report on the comparison of the strain field from numerical modelling forecasts against the experimental data obtained with the digital image correlation method under Mode II loading in fatigue testing. The numerical dual boundary element method has been established in the past as a very reliable method near singular regions where stresses tend to grow abruptly. The results obtained from the strain data near the crack tip were used in Williams expansion and agree fairly well with both the numerical results and the analytical solution proposed for pure Mode II testing.

The work presented in this note is experimental. The proposed methodology is of an hybrid experimental/numerical nature in that a numerical stress intensity factor calculation hinges upon a stress field obtained with an image method.

The obtained results are an important step towards the development of a practical tool for crack behaviour prediction in fatigue dominated events.

The results also stress the necessity of improving the experimental techniques to a point where the methods can be applied in real-life solicitations outside of laboratory premises.

Although several research teams around the globe are presently working in this field, the present research topic is original and the proposed methodology has been presented initially by the research team years ago.

This paper aims to focus on the hybrid numerical method for effective design of silicon micromotor.

In this work, the authors introduced finite element methods combined with LUA and Matlab. The paper focuses on analysis of electrostatic micromotor and uses computer simulation procedure leading to new structure design.

This strategy enables changing of all parameters of the micromotors MEMS. Moreover, this strategy allows for taking advantage of FEM, namely possibility of calculations of complicated geometries (different electromagnetic devices too) without additional operations.

A novel strategy in computer modeling of micromotor MEMS, based on the fast and very efficient hybrid method for analysis and design, is proposed.

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.

This study aims to perform a comprehensive investigation to model the thermal characteristics of a coupled conduction-radiation heat transfer in a two-dimensional irregular enclosure including a triangular-shaped heat source.

For this purpose, a promising hybrid technique based on the concepts of blocked-off method, FVM and DOM is developed. The enclosure consists of several horizontal, vertical and oblique walls, and thermal conductivity within the enclosure varies directly with temperature and indirectly with position. To simplify the complex geometry, a promising mathematical model is introduced using blocked-off method. Emitting, absorbing and non-isotropic scattering gray are assumed as the main radiative characteristics of the steady medium.

DOM and FVM are, respectively, applied for solving radiative transfer equation (RTE) and the energy equation, which includes conduction, radiation and heat source terms. The temperature and heat flux distributions are calculated inside the enclosure. For validation, results are compared with previous data reported in the literature under the same conditions. Results and comparisons show that this approach is highly efficient and reliable for complex geometries with coupled conduction-radiation heat transfer. Finally, the effects of thermo-radiative parameters including surface emissivity, extinction coefficient, scattering albedo, asymmetry factor and conduction-radiation parameter on temperature and heat flux distributions are studied.

In this paper, a hybrid numerical method is used to analyze coupled conduction-radiation heat transfer in an irregular geometry. Varying thermal conductivity is included in this analysis. By applying the method, results obtained for temperature and heat flux distributions are presented and also validated by the data provided by several previous papers.

The purpose of this paper is to propose a computational model for thin layers, for problems of linear time-dependent heat conduction. The thin layer is replaced by a zero-thickness interface. The advantage of the new model is that it saves the need to construct and use a fine mesh inside the layer and in regions adjacent to it, and thus leads to a reduction in the computational effort associated with implicit or explicit finite element schemes.

Special asymptotic models have been proposed for linear heat transfer and linear elasticity, to handle thin layers. In these models the thin layer is replaced by an interface with zero thickness, and specific jump conditions are imposed on this interface in order to represent the special effect of the layer. One such asymptotic interface model is the first-order Bövik-Benveniste model. In a paper by Sussmann et al., this model was incorporated in a FE formulation for linear steady-state heat conduction problems, and was shown to yield an accurate and efficient computational scheme. Here, this work is extended to the time-dependent case.

As shown here, and demonstrated by numerical examples, the new model offers a cost-effective way of handling thin layers in linear time-dependent heat conduction problems. The hybrid asymptotic-FE scheme can be used with either implicit or explicit time stepping. Since the formulation can easily be symmetrized by one of several techniques, the lack of self-adjointness of the original formulation does not hinder an accurate and efficient solution.

Most of the literature on asymptotic models for thin layers, replacing the layer by an interface, is analytic in nature. The proposed model is presented in a computational context, fitting naturally into a finite element framework, with both implicit and explicit time stepping, while saving the need for expensive mesh construction inside the layer and in its vicinity.

The purpose of this paper is to apply an efficient hybrid computational numerical technique, namely, q-homotopy analysis Sumudu transform method (q-HASTM) and residual power series method (RPSM) for finding the analytical solution of the non-linear time-fractional Hirota–Satsuma coupled KdV (HS-cKdV) equations.

The proposed technique q-HASTM is the graceful amalgamations of q-homotopy analysis method with Sumudu transform via Caputo fractional derivative, whereas RPSM depend on generalized formula of Taylors series along with residual error function.

To illustrate and validate the efficiency of the proposed technique, the authors analyzed the projected non-linear coupled equations in terms of fractional order. Moreover, the physical behavior of the attained solution has been captured in terms of plots and by examining the L₂ and L_∞ error norm for diverse value of fractional order.

The authors implemented two technique, q-HASTM and RPSM to obtain the solution of non-linear time-fractional HS-cKdV equations. The obtained results and comparison between q-HASTM and RPSM, shows that the proposed methods provide the solution of non-linear models in form of a convergent series, without using any restrictive assumption. Also, the proposed algorithm is easy to implement and highly efficient to analyze the behavior of non-linear coupled fractional differential equation arisen in various area of science and engineering.

This paper aims to present a new approach to the numerical solution of skin effect integral equations in cylindrical conductors. An approximate, but very simple and accurate method for calculating the current density distribution, skin-effect resistance and inductance, in pulse regime of cylindrical conductor, having a circular or rectangular cross-section, is considered. The differential evolution method is applied for minimization of error functional. Because of its application in the practice, the lightning impulse is observed. Direct and inverse fast Fourier transform is applied.

This method contributes to increasing of correctness and much faster convergence. As the electromagnetic field components depend on the current density derivation, the proposed method gives a very accurate solution not only for current density distribution and resistance but also for field components and for internal inductance coefficients. Distribution of current and electromagnetic field in bus-bars can be successfully determined if the proximity effect is included together with the skin effect in calculations.

The study shows the strong influence of direct lightning strikes on the distribution of electrical current in cables used in lightning protection systems. The current impulse causes an increase in the current density at all points of the cross-section of the conductor, and in particular the skin effect on the external periphery. Based on the data calculated by using the proposed method, it is possible to calculate the minimum dimensions of the conductors to prevent system failures.

There are a number of approximations of lightning strike impulse in the literature. This is a limiting factor that affects the reliability and agreement between measured data with calculated values.

In contrast with other methods, the current density function is approximated by finite functional series, which automatically satisfy wave equation and existing boundary conditions. It is necessary to minimize the functional. This approach leads to a very accurate solution, even in the case when only two terms in current approximation are adopted.

The integral transform method is employed for the hybrid numerical‐analytical solution of two‐dimensional, steady‐state heat conduction within extended surfaces of variable longitudinal profile and temperature dependent thermal conductivity. Numerical results are then obtainable with automatic accuracy, allowing for the establishment of benchmark results and for the validation of approximate solutions. Convergence rates are illustrated for longitudinal fins with trapezoidal and parabolic profiles, and for different values of the governing parameters, Biot number and aspect ratio. In addition, the classical one‐dimensional approximate solutions are critically examined for these typical non‐straight profiles, and the applicability limits are investigated.