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High resolution simulations of body-internal electric field strengths induced by magneto-quasistatic fields from wireless power transfer systems are computationally expensive. The exposure simulation can be split into two separate simulation steps allowing the calculation of the magnetic flux density distribution, which serves as input into the second simulation step to calculate the body-internal electric fields. In this work, the magnetic flux density is interpolated from in situ measurements in combination with the scalar-potential finite difference scheme to calculate the resulting body-internal field. These calculations are supposed to take less than 5 s to achieve a near real-time visualization of these fields on mobile devices. The purpose of this work is to present an implementation of the simulation on graphics processing units (GPUs), allowing for the calculation of the body-internal field strength in about 3 s.

This work uses the co-simulation scalar-potential finite difference scheme to determine the body-internal electric field strength of human models with a voxel resolution of 2 × 2 × 2 mm³. The scheme is implemented on GPUs. This simulation scheme requires the magnetic flux density distribution as input, determined from radial basis functions.

Using NVIDIA A100 GPUs, the body-internal electric field strength with high-resolution models and 8.9 million degrees of freedom can be determined in about 2.3 s.

This paper describes in detail the used scheme and its implementation to make use of the computational performance of modern GPUs.

This study aims to assess the robustness and accuracy of the face-centred finite volume (FCFV) method for the simulation of compressible laminar flows in different regimes, using numerical benchmarks.

The work presents a detailed comparison with reference solutions published in the literature –when available– and numerical results computed using a commercial cell-centred finite volume software.

The FCFV scheme provides first-order accurate approximations of the viscous stress tensor and the heat flux, insensitively to cell distortion or stretching. The strategy demonstrates its efficiency in inviscid and viscous flows, for a wide range of Mach numbers, also in the incompressible limit. In purely inviscid flows, non-oscillatory approximations are obtained in the presence of shock waves. In the incompressible limit, accurate solutions are computed without pressure correction algorithms. The method shows its superior performance for viscous high Mach number flows, achieving physically admissible solutions without carbuncle effect and predictions of quantities of interest with errors below 5%.

The FCFV method accurately evaluates, for a wide range of compressible laminar flows, quantities of engineering interest, such as drag, lift and heat transfer coefficients, on unstructured meshes featuring distorted and highly stretched cells, with an aspect ratio up to ten thousand. The method is suitable to simulate industrial flows on complex geometries, relaxing the requirements on mesh quality introduced by existing finite volume solvers and alleviating the need for time-consuming manual procedures for mesh generation to be performed by specialised technicians.

Magneto-quasi-static fields emanated by inductive charging systems can be potentially harmful to the human body. Recent projects, such as TALAKO and MILAS, use the technique of wireless power transfer (WPT) to charge batteries of electrically powered vehicles. To ensure the safety of passengers, the exposing magnetic flux density needs to be measured in situ and compared to reference limit values. However, in the design phase of these systems, numerical simulations of the emanated magnetic flux density are inevitable. This study aims to present a tool along with a workflow, based on the Scaled-Frequency Finite Difference Time-Domain and Co-Simulation Scalar Potential Finite Difference schemes, to determine body-internal magnetic flux densities, electric field strengths and induced voltages into cardiac pacemakers. The simulations should be time efficient, with lower computational costs and minimal human workload.

The numerical assessment of the human exposure to magneto-quasi-static fields is computationally expensive, especially when considering high-resolution discretization models of vehicles and WPT systems. Incorporating human body models into the simulation further enhances the number of mesh cells by multiple millions. Hence, the number of simulations including all components and human models needs to be limited while efficient numerical schemes need to be applied.

This work presents and compares four exposure scenarios using the presented numerical methods. By efficiently combining numerical methods, the simulation time can be reduced by a factor of 3.5 and the required storage space by almost a factor of 4.

This work presents and discusses an efficient way to determine the exposure of human beings in the vicinity of wireless power transfer systems that saves computer simulation resources and human workload.

The purpose of this study is to provide the enhancement of power quality of a high power-rated voltage source inverter driven induction motor with a three-phase, three-level neutral point clamped converter placed at the front end, while a passive power filter is connected in shunt with it. The improvement in power quality can be achieved by reducing the total harmonic distortion in source current. The controllers were designed for the linearization of the high-power induction motor drive. A control method is presented for the regulation of the common DC-link voltage.

The induction motor is modeled using its dynamic equations, and a decoupling controller is designed to linearize the nonlinear dynamics of the drive through feedback. The common DC-link voltage of the proposed front-end connected converter is monitored and controlled through a control method which feeds the pulse width modulated inverter that drives the induction motor. A passive power filter is designed to meet the reactive power requirement of the system in addition to improve the power quality.

Simulations were carried out for the proposed topology of the drive mechanism, and the outcomes were analyzed by a comparative analysis of the drive system both in the presence of the passive filter as well as in the absence of the filter. The total harmonic distortion is found to be reduced enough to meet the standards with the designed filter, and the reactive power is also compensated considerably. The input power factor at the supply side is maintained almost to unity, and the DC-link voltage of the proposed circuit topology is maintained at the desired level. The overall performance of the drive system was found to be useful and economical.

A new topology of a front-end connected three-level neutral point clamped converter to a high power-rated induction motor drive is proposed. The drive is fed by a pulse width modulated inverter with a common DC-link with the front end connected converter. A passive filter is designed with respect to the reactive power requirement of the system and connected in shunt to the converter at the supply side. Control schemes are designed and used for the drive system and also for the regulation of the common DC-link voltage of the proposed front end connected converter.

In this study, the authors propose a novel digital twinning approach specifically designed for controlling transient thermal systems. The purpose of this study is to harness the combined power of deep learning (DL) and physics-based methods (PBM) to create an active virtual replica of the physical system.

To achieve this goal, we introduce a deep neural network (DNN) as the digital twin and a Finite Element (FE) model as the physical system. This integrated approach is used to address the challenges of controlling an unsteady heat transfer problem with an integrated feedback loop.

The results of our study demonstrate the effectiveness of the proposed digital twinning approach in regulating the maximum temperature within the system under varying and unsteady heat flux conditions. The DNN, trained on stationary data, plays a crucial role in determining the heat transfer coefficients necessary to maintain temperatures below a defined threshold value, such as the material’s melting point. The system is successfully controlled in 1D, 2D and 3D case studies. However, careful evaluations should be conducted if such a training approach, based on steady-state data, is applied to completely different transient heat transfer problems.

The present work represents one of the first examples of a comprehensive digital twinning approach to transient thermal systems, driven by data. One of the noteworthy features of this approach is its robustness. Adopting a training based on dimensionless data, the approach can seamlessly accommodate changes in thermal capacity and thermal conductivity without the need for retraining.

This paper aims to present an unconditionally energy-stable scheme for approximating the convective heat transfer equation.

The scheme stems from the generalized positive auxiliary variable (gPAV) idea and exploits a special treatment for the convection term. The original convection term is replaced by its linear approximation plus a correction term, which is under the control of an auxiliary variable. The scheme entails the computation of two temperature fields within each time step, and the linear algebraic system resulting from the discretization involves a coefficient matrix that is updated periodically. This auxiliary variable is given by a well-defined explicit formula that guarantees the positivity of its computed value.

Compared with the semi-implicit scheme and the gPAV-based scheme without the treatment on the convection term, the current scheme can provide an expanded accuracy range and achieve more accurate simulations at large (or fairly large) time step sizes. Extensive numerical experiments have been presented to demonstrate the accuracy and stability performance of the scheme developed herein.

This study shows the unconditional discrete energy stability property of the current scheme, irrespective of the time step sizes.

This paper aims to study passive control techniques for transonic flow over a backward-facing step (BFS) using square-lobed trailing edges. The study investigates the efficacy of upward and downward lobe patterns, different lobe widths and deflection angles on flow separation, aiming for a deeper understanding of the flow physics behind the passive flow control system.

Large Eddy Simulation and Reynolds-averaged Navier–Stokes were used to evaluate the results of the study. The research explores the impact of upward and downward patterns of lobes on flow separation through the effects of different lobe widths and deflection angles. Numerical methods are used to analyse the behaviour of transonic flow over BFS and compared it to existing experimental results.

The square-lobed trailing edges significantly enhance the reduction of mean reattachment length by up to 80%. At Ma = 0.8, the up-downward configuration demonstrates increased effectiveness in reducing the root mean square of pressure fluctuations at a proximity of 5-step height in the wake region, with a reduction of 50%, while the flat-downward configuration proves to be more efficient in reducing the root mean square of pressure fluctuations at a proximity of 1-step height in the near wake region, achieving a reduction of 71%. Furthermore, the study shows that the up-downward configuration triggers early spanwise velocity fluctuations, whereas the standalone flat-downward configuration displays less intense crosswise velocity fluctuations within the wake region.

The findings demonstrate the effectiveness of square-lobed trailing edges as passive control techniques, showing significant implications for improving efficiency, performance and safety of the design in aerospace and industrial systems.

This paper demonstrates that the square-lobed trailing edges are effective in reducing the mean reattachment length and pressure fluctuations in transonic conditions. The study evaluates the efficacy of different configurations, deflection angles and lobe widths on flow and provides insights into the flow physics of passive flow control systems.

The purpose of this paper is to address unsteady heat conduction in two subsets of ordinary bodies. One subset consists of a large plane wall, a long cylinder and a sphere in one dimension. The other subset consists of a short cylinder and a large rectangular bar in two dimensions. The prevalent assumptions in the two subsets are: constant initial temperature, uniform surface heat flux and thermo-physical properties invariant with temperature. The engineering applications of the unsteady heat conduction deal with the determination of temperature–time histories in the two subsets using electric resistance heating, radiative heating and fire pool heating.

To this end, a novel numerical procedure named the enhanced method of discretization in time (EMDT) transforms the linear one-dimensional unsteady, heat conduction equations with non-homogeneous boundary conditions into equivalent nonlinear “quasi–steady” heat conduction equations having the time variable embedded as a time parameter. The equivalent nonlinear “quasi–steady” heat conduction equations are solved with a finite difference method.

Based on the numerical computations, it is demonstrated that the approximate temperature–time histories in the simple subset of ordinary bodies (large plane wall, long cylinder and sphere) exhibit a perfect matching over the entire time domain 0 < t < ∞ when compared against the rigorous exact temperature–time histories expressed by classical infinite series. Furthermore, using the method of superposition of solutions in the convoluted subset (short cylinder and large rectangular crossbar), the same level of agreement in the approximate temperature–time histories in the simple subset of ordinary bodies is evident.

The performance of the proposed EMDT coupled with a finite difference method is exhaustively assessed in the solution of the unsteady, one-dimensional heat conduction equations with prescribed surface heat flux for: a subset of one-dimensional bodies (plane wall, long cylinder and spheres) and a subset of two-dimensional bodies (short cylinder and large rectangular bar).

The purpose of this study is to investigate the interaction between magnetotactic bacteria and Fe₃O₄–water nanofluid (NF) in a wavy enclosure in the presence of 2D natural convection flow.

Uniform magnetic field (MF), Brownian and thermophoresis effects are also contemplated. The dimensionless, time-dependent equations are governed by stream function, vorticity, energy, nanoparticle concentration and number of bacteria. Radial basis function-based finite difference method for the space derivatives and the second-order backward differentiation formula for the time derivatives are performed. Numerical outputs in view of isolines as well as average Nusselt number, average Sherwood number and flux density of microorganisms are presented.

Convective mass transfer rises if any of Lewis number, Peclet number, Rayleigh number, bioconvection Rayleigh number and Brownian motion parameter increases, and the flux density of microorganisms is an increasing function of Rayleigh number, bioconvection Rayleigh number, Peclet number, Brownian and thermophoresis parameters. The rise in buoyancy ratio parameter between 0.1 and 1 and the rise in Hartmann number between 0 and 50 reduce all outputs average Nusselt, average Sherwood numbers and flux density of microorganisms.

This study implies the importance of the presence of magnetotactic bacteria and magnetite nanoparticles inside a host fluid in view of heat transfer and fluid flow. The limitation is to check the efficiency on numerical aspect. Experimental observations would be more effective.

In practical point of view, in a heat transfer and fluid flow system involving magnetite nanoparticles, the inclusion of magnetotactic bacteria and MF effect provide control over fluid flow and heat transfer.

This is a scientific study. However, this idea may be extended to sustainable energy or biofuel studies, too. This means that a better world may create better social environment between people.

The presence of magnetotactic bacteria inside a Fe₃O₄–water NF under the effect of a MF is a good controller on fluid flow and heat transfer. Since the magnetotactic bacteria is fed by nanoparticles Fe₃O₄ which has strong magnetic property, varying nanoparticle concentration and Brownian and thermophoresis effects are first considered.

This paper focuses on the unconditionally optimal error estimates of a linearized second-order scheme for a nonlocal nonlinear parabolic problem. The first step of the scheme is based on Crank–Nicholson method while the second step is the second-order BDF method.

A rigorous error analysis is done, and optimal L² error estimates are derived using the error splitting technique. Some numerical simulations are presented to confirm the study’s theoretical analysis.

Optimal L² error estimates and energy norm.

The goal of this research article is to present and establish the unconditionally optimal error estimates of a linearized second-order BDF finite element scheme for the reaction-diffusion problem. An optimal error estimate for the proposed methods is derived by using the temporal-spatial error splitting techniques, which split the error between the exact solution and the numerical solution into two parts, that is, the temporal error and the spatial error. Since the spatial error is not dependent on the time step, the boundedness of the numerical solution in L∞-norm follows an inverse inequality immediately without any restriction on the grid mesh.