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In the present study, a novel application of integrated evolutionary computing paradigm is presented for the analysis of nonlinear systems of differential equations representing the dynamics of virus propagation model in computer networks by exploiting the discretization strength of finite difference procedure, global search efficacy of genetic algorithms (GAs) aided with interior-point method (IPM) as efficient local search mechanism. Residual error based cost function is constructed by utilizing the effectiveness of approximation in mean square error sense and combined strength of GA-IPM is used as a viable optimization mechanism to find the solution of the problem. The proposed scheme is implemented for dynamical analysis of the model in terms of susceptible-infected and protected computer nodes by varying the probabilities of infections, countermeasures, curing and immunity while keeping connected and disconnected rates fixed. The statistical performance evaluated by means of deviations from reference Adams numerical results are practiced viably through performance metrics of accuracy and computational complexity to demonstrate the worth of integrated stochastic solver.

This study aims to propose a set of time-dependent chloride transport models based on the measured data of 16 locations of monolithic concrete bridge decks under the attack of chloride ions in form of de-icing salts. This is carried out due to the shortcomings in the previous study which developed time-independent models containing two regression parameters. In this study, there are four regression parameters to be determined. They are simultaneously calculated using the finite difference formulation embedded with regression analysis. From the study, it is observed that the developed chloride transport model can predict the chloride content in most bridge decks. Although the prediction in some cases falls outside 50% margin of difference, they are on the conservative side. The regression parameters in the surface chloride function calculated here is higher than those in the previous study by two times. Seemingly, the diffusion coefficient in this study is comparable with that in Life-365 program. On the measurement or field survey date, if using the critical chloride value of 0.6 and 1.2 kg/m3, most and 5 of 16 bridge decks, respectively, would have rebar corrosion. However, there would be no concrete cracking if using the critical chloride value of 2.0 kg/m3.

Current design constraints have encouraged the studies of aeroacoustics fields around compressible jet flows. The present work addresses the numerical study of unsteady turbulent jet flows for aeroacoustic analyses of main engine rocket plumes. A novel large eddy simulation (LES) tool is developed in order to reproduce high fidelity results of compressible jet flows which could be used for aeroacoustic studies with the Ffowcs Williams and Hawkings approach. The numerical solver is an upgrade of an existing Reynolds-averaged Navier-Stokes solver previously developed in the group. The original framework is rewritten in a modern fashion and intensive parallel computation capabilities have been added to the code. The LES formulation is written using the finite difference approach. The energy equation is carefully discretized in order to model the energy equation of the filtered Navier-Stokes formulation. The classical Smagorinsky model is the chosen subgrid scale closure for the present work. Numerical simulations of perfectly expanded jets are performed and compared with the literature in order to validate the new solver. Moreover, speedup and the computational performance of the code are evaluated and discussed. Flow results are used for an initial evaluation of the noise radiated from the rocket plume., 25 pages conference paper

Experimental evidence shows that a beam that can develop a flexural mechanism of failure under static load may fail in shear under blast load during its initial stages of response. Shear failure limits the ability of the beam to “absorb” the energy imparted by blast load. Because energy-absorption capacity is the key to the survival of a structural element to blast, initial shear failure must be avoided. To do so, the likelihood of a change in the failure mechanism (from flexure to shear) of a beam under blast load must be quantified. This can be done by evaluating the ratio of initial shear demand to shear capacity for the beam. The matter is not as simple as it may appear because, for dynamic and impulsive load, shear demand depends on inertial forces and shear capacity depends on loading rate. This paper presents the results of analytical and numerical investigations conducted to characterize the initial response and provide simple means to estimate initial shear demand in beams subjected to blast. Two simple numerical methods are used to estimate shear demand: (1) a finite difference-based solution of the equations of motion of a linear Timoshenko beam; and (2) a method proposed by the authors based on an equivalent linear single-degree-of-freedom (SDOF) system and the work done by Biggs (1964) to compute dynamic reactions. The results for maximum shear obtained with both methods are compared with results from finite element analysis (FEA) of beams subjected to blast. Initial shear response of one-way reinforced concrete slabs tested under blast load is also analyzed using the two simple methods. It is shown that these methods provide results that are in reasonable agreement with FEA results and experimental observations, which makes them suitable for preliminary blast-resistant design, especially considering their simplicity.

The risk of TBM shield jamming in jointed rocks is one of the main concerns in the deep tunnel construction. To realistically evaluate the possibility of shield jamming in such grounds, the property of joint sets, the behavior of jointed rocks and the interaction between the rocks and shields, segmental lining and backfilling need to be understood. Referring to these finite element models and finite difference models, a combined discrete element-finite difference model for simulating double-shield TBM excavation in jointed rocks is developed in 3DEC. To describe the behavior of jointed rocks realistically, a fish code is written in 3DEC to generate random joints considering their orientation, spacing, position and persistence. The orientation and spacing are assumed to obey Fisher distribution and uniform distribution, respectively, and then the position is determined by the corresponding orientation and spacing. Moreover, the zone of jointed rocks around the tunnel is modeled by discrete element model, while the other zones, such as the jointed rocks away from the tunnel and the hard rocks, are modeled by finite difference model, which can effectively reduce the computer runtime and hardware resource. The severest shield jamming of the DXL tunnel excavated by a double-shield TBM is conducted to demonstrate the applicability of the proposed model. The results are more consistent with the failure phenomenon on site than the finite element model or finite difference model. The proposed model can be used to quantitatively evaluate the potential risk of TBM jamming in jointed rocks.

In this paper, the elastic-plastic analysis of cantilever beam and the Reinforced Concrete (RC) column-Steel (S) beam connection are studied using the Radial Basis Function- Finite Difference (RBF-FD) method. A direct method using bilinear nodes is proposed to deal with the instability caused by the first derivative calculation in the traditional RBF-FD method. Based on the idea of gradient projection method, the improved RBF-FD method is further applied to the multi-domain material nonlinearity. Numerical results are validated with the finite element method software (COMSOL).

The post-peak response of elasto-plastic material is dependent upon the stress path it is subjected to. This paper analyses and compares the stress path and strain response of advancing tunnel, using two-dimension:1al plane strain (2D PS) and full three-dimensional step by step excavation and support (3D SBS) finite difference numerical model (FDM). Stress paths for 3D SBS model indicate higher stress relaxation and straining at unsupported spans as well as elastic recompression behind applied supports; these features are not evident in 2D PS models. Implications of these differences on tunnel response are discussed. The complex 3D stress evolution with tunnel construction is greatly simplified by considering major and minor principal stresses only, for the purpose of stress path generation. To verify that the formulation of stress path adopted here is sufficient to describe stress–strain evolution of 3D SBS tunnel model, a numerical simulation of “stress path following triaxial unloading test” is conducted using “simplified loading conditions.” Results show that the suggested test methodology has potential to map stress path of 3D SBS tunnel model for ideal geomaterial behavior. Also, improvement in measured strain response, as compared to 2D PS models, is observed.

In the literature, several techniques are implemented to obtain the approximate solution of heat and advection–diffusion equations. However, each method involves certain drawbacks such as high arithmetic computations, lower accuracy in terms of error, and difficult for computer programming. In the present work, the octic B-spline collocation approach is implemented to incorporate the drawback of the other numerical studies in the literature with with high accuracy in terms of error and MATLAB programming is executed to compute the tedious calculation in an easy way toward the improvement of the approximate solution of heat and advection–diffusion equation. The time derivative is discretized by forward difference technique and the Crank–Nicolson scheme is applied for the remaining terms of the advection–diffusion equation. The stability of the scheme is examined and found that the scheme is unconditionally stable. To test the accuracy and efficiency of the scheme, four test problems are computed. A better approximate solution is obtained as compared to existing methods and a good agreement on analytical solutions by the proposed scheme.

Among vibration-based damage detection methods, one of the effective approaches for damage localization is the modal strain energy method. In this paper, the modal strain energy method is developed for damage detection in plate-like structures with various boundary conditions. Firstly, the theory of the modal strain energy method is briefly outlined. In order to overcome the limitation of measuring points, a central difference method is newly employed to compute the partial differential terms in the modal strain energy formula. Finite element analysis is conducted on an aluminum thin plate to obtain the mode shapes before and after the occurrence of damage. Feasibility of the proposed method is verified by investigating plates with different types of boundary conditions. A damage index is presented to identify the location and extent of crack in the plate-like structures. The analytical results show that the proposed method accurately identifies the crack in the plate structure with various types of boundary conditions by using appropriate mode shapes and damage threshold.

Energy recovery ventilators are often employed in buildings to decrease the energy consumed by their HVAC systems, and to improve overall indoor air quality. Several studies in the open literature have developed physical or empirical models to simulate the performance of energy recovery wheels. However, these models are often computationally intensive, time-consuming, or require numerous experimental data points to train and execute the performance predictions. These models also tend to lack flexibility for varying all of the available wheel design parameters. Hence, developing a mapping method with better computational efficiency and flexibility is the goal of this research. A finite difference numerical model for simulating the performance of an energy wheel has been developed and validated using experimental test results from independent laboratories. This model was then employed to provide an extensive data set for the development of an energy wheel performance mapping method. After validating this new mapping approach, the method predictions were compared against independent data sets from two different laboratories, and additional sources available in the literature, to identify its universality. The mapping method delivers good agreement between the predictions and validation data, and requires only a small number of data points to train, which is one of its novel contributions. Another unique contribution of the proposed mapping method is that once the model is trained it can predict the performance characteristics for other wheels with different physical design geometries and operating conditions, provided only that the desiccant material is the same.

In this work, nanofluid’s stagnation point flow is studied considering a stretchable cylinder that is oriented vertically with the perspective of application in irrigation systems and biotechnology. The study carried the modified Fourier’s flux and buoyancy force. The prescribed surface temperature (PST) is utilized. The governing PDEs initially transformed into ODE. A numeric technique based on the Newton forward difference scheme is used to feature extraction of velocity, concentration, and temperature against the parameters having physical worth. The outcomes are studied through sketching the graphs of numeric data received. We perceived that the higher value of the unsteadiness parameter reduces the velocity, temperature, and concentration profile while the enhancing buoyancy boosted the velocity profile.

The behavior of retaining walls in geosynthetic reinforced soil is complex and requires studies and research to understand the mechanisms of rupture, the behavior of the reinforcements in the soil and the behavior of the main elements of the system: reinforcement-wall-soil. Several researches have been done on the use of geosynthetics as backfill massive reinforcement material (experimental studies, numerical analysis, reduced models …). This parametric study was conducted to investigate the influence of modular blocks type on the behavior of reinforced soil segmental walls. A 3.6 m high wall is composed of modular blocks of earth sand reinforced with four geogrid layers was modeled. The properties of materials, the wall geometry, and the boundary conditions will be explained later. The finite difference computer program FLAC3D was used in this study. The results of this numerical study allowed deducing the importance of this parameter. The type of modular blocks has significant effect to decrease the values of lateral displacements of the wall and decreased tensile stress values in the layers of geogrid.

The human thermal comfort is the state of mind, which is affected not only by the physical and body’s internal physiological phenomena but also by the clothing properties such as thermal resistance of clothing, clothing insulation, clothing area factor, air insulation, and relative humidity. In this work, we extend the one-dimensional Pennes’ bioheat transfer equation by adding the protective clothing layer. The transient temperature profile with the clothing layer at the different time steps has been carried out using a fully implicit Finite Difference (FD) Scheme with interface condition between body and clothes. Numerically computed results are bound to agree that the clothing insulation and air insulation provide better comfort and keep the body at the thermal equilibrium position. The graphical representation of the results also verifies the effectiveness and utility of the proposed model.

Real-time fault monitoring and control of the Vacuum Assisted Resin Transfer Moulding production process requires knowledge of the position of the epoxy flow-front inside the mould. Therefore, a fast and accurate flow-front tracking system is highly prized. Physics-informed grey-box models deliver a good trade-off between high fidelity and data-driven black-box models for designing such a flow-front tracking system. In this paper, we propose stochastic differential equations (SDEs) based grey-box model of the flow-front dynamics in the case of missing sensor information. The proposed method uses the finite difference approximation of the spatial domain of the flow-front for estimating the spatial flow pattern of the epoxy. To accommodate for the missing sensor data, we utilize a modified version of the continuous-discrete extended Kalman filter based estimation framework for SDEs that takes into consideration the effective dimension of the measurement space during the identification process. The performance of the method is evaluated for common fault scenarios.

Automotive powertrain mounting systems (PMSs) may exhibit hybrid interval-random (HIR) uncertainties in engineering practice. In HIR case, the uncertain parameters of PMSs are characterized as the random variables with interval distributions. A comprehensive methodology is proposed for the design optimization of the PMSs involving HIR uncertainties in this study. The hybrid interval-random perturbation central difference method (HIRP-CDM) is firstly derived to calculate the uncertain responses of PMSs, in which HIR uncertainties are addressed by twice perturbation analyses and twice central difference analyses. Meanwhile, the hybrid interval-random Monte Carlo method is presented as a reference method. Then, reliability assessment models are constructed to evaluate the probability intervals of system inherent characteristics satisfying design requirements. Next, a design optimization model is formulated to explore the optimal design of PMSs. The expectation intervals and variance intervals of system inherent characteristics are taken to create optimization objective, and the minimal probabilities of system inherent characteristics meeting requirements are utilized to establish reliability constraints. Both robustness and reliability are considered in the optimization, and the optimization can be simplified with the aid of HIRP-CDM. The effectiveness of the proposed methodology is finally demonstrated by the numerical example.

In urban areas, the construction of subway tunnels is faced with complex crossing problems. The interaction of tunnels with structural deformation has not been comprehensively studied, especially in the construction of new tunnels crossing above existing tunnels. To better predict the structural deformation of the existing tunnels caused by shield excavation, this study used FLAC3D finite difference software, field monitoring, and an analytical method. A numerical model was used to simulate the influence of the shield weight, grouting pressure, and the grout hardening process on the existing tunnel. The results show that the deformation of horseshoe-shaped tunnel structure can be divided into four stages and the corresponding control measures should be taken for each stage to prevent the structural damage. Moreover, the weight of the shield can restrain the existing tunnel from floating up, but it may cause the cracking of the existing tunnel structure without internal steel support. Based on the “two-stage analysis method”, the simplified analytical method solved the additional stress and the uplift deformation in the first stage and second stage, respectively. The proposed analytical method can rapidly estimate the maximum uplift deformation of the existing horseshoe-shaped tunnel with different bending stiffness values under shield excavation.

The flow through partially-open control valves in navigation locks, particularly at the early portion of an operation cycle, is characterized by high velocities, flow recirculation, significant pressure drops, and pressure fluctuations within the culverts. Optimizing the flow control system is a key point in hydraulic projects of high-drop locks. In order to analyze the hydraulic parameters of the mean flow and turbulence statistics through a navigation lock control valve, experimental and numerical work was undertaken. This paper focuses on the numerical aspects of the research. A physical model with a rectangular culvert (25 cm x 25 cm) test section with a segment gate (Tainter) installed in its inverted position was used in the experimental research. Physical tests were carried out under steady conditions for six gate openings and nine discharges. During these tests, mean and instantaneous pressures were recorded along the base and the ceiling of the culvert. The numerical investigation was carried out using the Computational Fluid Dynamics (CFD) software FLOW- 3D®. In FLOW- 3D®, the Reynolds-Averaged Navier–Stokes (RANS) equations were solved by the methods of finite volumes/finite differences in two dimensions. To solve the problem of closing RANS equations, the turbulence model k − e was adopted. Based on the results, it was possible to verify that the numerical model very nicely reproduced the behavior of experimental data of mean hydraulic head and mean flow velocities. Although along the culvert ceiling, particularly close to the gate, the drop in mean pressure was slightly underestimated by the numerical model at the flow recirculating zone, it is possible to state with confidence that the overall results underscore the accuracy of this CFD approach in the study of the mean flow downstream from the control valves in navigation lock filling–emptying systems.

A nonlinear analysis framework for laterally loaded piles is presented that is as accurate as equivalent three-dimensional nonlinear finite element analysis, but computationally one order of magnitude faster. The nonlinear behavior of sands and clays are account for by using hyperbolic modulus–reduction relationships. These nonlinear–elastic constitutive models are used to calculate the reduced modulus at different points in the soil based on the soil strains induced by lateral pile displacement. The reduced modulus at different points in the soil domain are spatially integrated to calculate the reduced soil resistance parameters associated with the differential equation governing the lateral pile displacement. The differential equations governing the lateral displacements of pile and soil under equilibrium are obtained by applying the principle of virtual work to a continuum-based pile–soil system. These coupled differential equations are solved using the one-dimensional finite difference method following an iterative algorithm. The accuracy of the analysis is verified against equivalent three-dimensional nonlinear finite element analysis, and the validity of the analysis in predicting the field response is checked by comparisons with multiple pile load test results. Parametric studies are performed to gain insights into the lateral pile response.

Accurately estimating load distributions and ground responses around underground openings plays a significant role in the safety of the operations in underground mines. Adequately designing pillars and other support measures relies highly on the accurate assessment of the mining-induced loads, as well as the load-bearing capacities of the supports. There are various methods that can be used to approximate mining-induced loads in stratified rock masses, both empirical and numerical. In this study, the numerical modeling approach recently developed at West Virginia University, which is based on the modeling approach developed by the National Institute for Occupational Safety and Health (NIOSH), is investigated using the finite difference software FLAC3D. The model includes the longwall panels, the adjacent chain pillar systems, and the different stratigraphic layers of the overburden. Using the 3D model, changes in loading conditions and deformations on the areas of interest, induced by an approaching longwall face, can be examined. This paper details the 3D modeling of a longwall panel utilizing this approach, and the verification of the results against field observations. The studied panel was 360 m wide with a 3-entry chain pillar system and about a 160-m average overburden depth around the studied area. The overburden strata consist of alternating layers of shale, sandstone, and limestone. The FLAC3D results were compared against field measurements from the mine site. The stress change values measured in the chain pillars were comparable with the modeling results. The model also replicated the surface subsidence profile obtained from field measurements fairly well. Overall, the 3D modeling approach was found to be successful for the case study longwall panel.

One of the major challenges in increasing the efficiency of the CZTSSe solar cells is to control the lattice defects formation and secondary phases in the absorber layer of the cells. Moreover, by controlling and decreasing lattice defects and thus improving the efficiency, larger-scale applications would be financially acceptable. In this paper, several CZTSSe thin-film solar cells have been prepared and one device with champion efficiency of 10.33% has been chosen for the modeling. Afterward, numerical simulations based on the Finite Element Method (FEM) and Finite Difference (FD) were conducted on these cells. The effect of defects density and defect types, which are located at different energy levels in the absorber layer bandgap, was evaluated. The results indicated that by decreasing the defects which are located close to the electron Fermi level and the middle of the band gap ( E g / 2 ), the maximum efficiency of 18.47% for these solar cells can be achieved.

Buckling of uniformly and not uniformly compressed tower buildings, resting on Winkler type soil, is investigated. An equivalent beam is introduced, able to capture the essential behavior of the building. It is a 3D Timoshenko beam, modeled in the framework of a direct approach, whose constitutive law is derived via a homogenization procedure, which includes the effect of the column prestress. The continuous model is discretized via finite differences, and a linear bifurcation analysis is carried out by solving an algebraic eigenvalue problem. Numerical results are shown for sample problems, aimed at detecting the structural behavior, and illustrating the role of some mechanical parameters. Results supplied by the equivalent beam model are compared with those derived by finite element analyses, carried out on three-dimensional frames.

Star sensors are easily disturbed by stray light when working in the space environment: the quality of star image can be seriously reduced and the difficulty of star image preprocessing can be greatly increased. In this paper we propose a novel method for eliminating stray light interference based on the grayscale difference of star images. Firstly, since the grayscale difference between the edge of a star spot and the surrounding background pixels was very large, a grayscale forward difference was performed on the star image row by row. Based on the equivalent difference star image obtained, we could propose an edge pixel criterion for the star spot. Secondly, Stray light interference was eliminated from the star image through a connected component analysis based on the edge pixels criterion for the star spot. The relatively complete star spot areas were marked on the marker map. The simulation results demonstrate that the star spot extraction rate achieved through the proposed method was much higher than that obtained through traditional star image preprocessing methods. As long as the star spot is not submerged by the stray light, the proposed method is robust enough to ensure a successful extraction of the star spot.

Typically, hydrocarbon reservoirs have heterogeneities that influence pressure variation in producing wells. In the case of natural fractures, the layer model has been widely applied to obtain analytical and numerical solutions. In this model, we superimpose the porous media layers representing the porous matrix and fractures. In this work, the layer model is used in the numerical simulation, using cylindrical geometry and finite differences, to determine the pressure in natural gas producing wells. We consider shale gas reservoirs, and obtain the numerical results investigating the effects resulting from the presence of fractures and non-Darcy flow due to slip and adsorption phenomena. This work studies grid refinement and performs numerical verification, as well as a sensitivity analysis varying the main physical parameters that directly influence the reservoir and well pressures, such as permeability, porosity, and thickness of the fracture, reservoir temperature, and the Langmuir pressure and volume. As expected, from specialized and diagnostic plots, we can visualize how fractures favor the flow while capturing typical flow regimes of fractured reservoirs described in the literature.

A numerical approach, the Hyperstatic Reaction Method (HRM), is presented in this paper to study the behavior of two kinds of U-shaped tunnel linings (with and without an inverted arch). The developed numerical HRM model is validated by a comparison with the results obtained from finite difference numerical models using FLAC3D. The results of this paper show that the behavior of U-shaped tunnel supports could be effectively estimated by the proposed HRM model. Using the HRM model, the effect of the shear springs and the toe constraint on the behavior of U-shaped tunnel linings without an invert are studied. In addition, the results of two kinds of U-shaped tunnels obtained by the HRM are compared with those of a circular-shaped kind. A parametric investigation is conducted considering the changes in the stiffness of the springs, the loads on the supports, the geometries, and the bending stiffness of the support structures.

Purpose The purpose of this paper is to shed some light into the equivalency of grid size and spatial and temporal orders of accuracy for turbulent flows. Design/methodology/approach This paper compared several finite difference schemes on various meshes and various orders of accuracy for the canonical Taylor–Green vortex testcase. Findings A remarkable empirical result observed is that the accuracy of eighth-order schemes on grids of size 2 h was equivalent to second-order schemes on grids of size h. This was the case when going from 1003 to 2003 as well as from 2003 to 4003. In all these cases, kinetic energy, vorticity and numerical dissipation were compared in detail. Research limitations/implications The results obtained were carried out using finite difference solvers. It remains to be seen if similar behaviors are also observed for other numerical schemes. Originality/value These (surprising) findings should be of interest to the larger community.

Shale gas resources (SGR), as a representative of natural gas hydrate reservoirs, have been the main energy supply for the energy consumption currently. The multi-scale pore structure of shale, complicated seepage mechanisms, including Knudsen diffusion, matrix deformation, stress sensitivity, non-Darcy flow and spatial fracture network stimulated by hydraulic fracturing technology have posed huge challenges to an accurate prediction and assessment of shale gas recovery. A full understanding of gas seepage mechanism of shale gas is the critical and scientific issue to develop carbon hydrogen energy resources effectively. It is very urgent to establish a comprehensive mathematical model to analyze the productivity capacity through simultaneously considering various flow mechanisms and fractures network system. To fill this gap, this paper presents a comprehensive numerical model of hydraulic fracturing horizontal well with discrete fracture network where embedded discrete fracture model (EDFM) is employed to characterize the coupled phenomenon between discrete fracture network and fractured SGR. And then two numerical discretization methods, e.g., finite difference and finite-volume, are used to numerically discretize the equations, subsequently, the Newton-Raphson iterative method is adopted to obtain the final solutions. Finally, the sensitivity analysis experiments are employed to investigate the effects of the key parameters. The results can provide some certain guidance for the optimization of stimulated treatment in natural gas hydrate reservoirs.

Essentially non-oscillatory (ENO) and weighted ENO (WENO) schemes were designed for solving hyperbolic and convection–diffusion equations with possibly discontinuous solutions or solutions with sharp gradient regions. The main idea of ENO and WENO schemes is actually an approximation procedure, aimed at achieving arbitrarily high-order accuracy in smooth regions and resolving shocks or other discontinuities sharply and in an essentially non-oscillatory fashion. Both finite volume and finite difference schemes have been designed using the ENO or WENO procedure, and these schemes are very popular in applications, most noticeably in computational fluid dynamics but also in other areas of computational physics and engineering. Since the main idea of the ENO and WENO schemes is an approximation procedure not directly related to partial differential equations (PDEs), ENO and WENO schemes also have non-PDE applications. In this paper we will survey the basic ideas behind ENO and WENO schemes, discuss their properties, and present examples of their applications to different types of PDEs as well as to non-PDE problems.

The article addresses the relevant issue of determining the thermotechnical characteristics of the fire-extinguishing powder for thermal insulation of the fire center of materials based on magnesium alloy chips to prevent fire development and propagation and its effective extinguishing. To solve this problem, laboratory and field experimental studies of the heat-insulating ability of the fire-extinguishing powder of combined effect were conducted. As a result, we obtained the data on the temperature in the center of the fire of materials based on magnesium alloy chips and outside during their suppressing by the fire-extinguishing powder with a combined effect. In this case, the temperature of the non-heated side of the fire-extinguishing powder layer does not exceed 170°C at the average temperature of the fire center of 740°C, which indicates high insulation capacity of the powder and, consequently, its high fire-fighting efficiency in extinguishing the fires of materials based on magnesium alloy chips. The obtained temperature data were used to determine the thermophysical parameters of the layer of the fire-fighting powder using the created mathematical model of the heat transfer process in the powder layer at the heat insulation of the fire center. To create a mathematical model of the heat transfer process, the main provisions during consecutive consideration of several experimental situations were stated. The first experimental situation meets the conditions of the stationary thermal process, and other experimental situations meet the conditions of the non-stationary thermal process. These experimental situations were created with the help of changing the thickness of the fire-fighting powder layer at different parameters of its feeding to the fire center. The mathematical model of the process is based on the use of the differential equation of heat transfer at its approximation by the method of finite differences. At the same time, it is believed that the heat transfer conditions at the boundary between the non-heated side of the insulating layer of the fire-extinguishing powder and the environment in each experimental situation are the same. Using the created model, the coefficient of heat transfer between the non-heated side of the insulating layer of the fire-extinguishing powder and the environment was determined. It amounted to 395.7W(m2×°С). The dependence of the effective thermal conductivity coefficient on the thickness of the insulating layer was explored. It was shown that this dependence can be approximated by linear dependence l(d)=–0.016+93.907×d (d is the thickness of the layer of the fire-extinguishing powder in meters). After conducting the necessary calculations, we obtained the value of the required thickness of the layer of fire-extinguishing powder d=45.2mm

The analysis of tunnel extrusion during full-face excavation necessitates a fully three-dimensional modeling which requires much effort to develop a numerical model and is thus very time-consuming, in particular, for complex cases to study the effect of face reinforcement by fiberglass bolts. It is, therefore, very useful to be able to dispose of a simplified tool permitting to make such evaluative analysis rapidly, in particular at the preliminary design stage. This paper presents a finite difference solution (FDM) for a spherical cavity reinforced by passive bolts in either brittle–plastic or strain-softening infinite medium subjected to a homogeneous initial stress field. Both linear Mohr–Coulomb (M–C) and nonlinear generalized Hoek–Brown (H–B) failure criterion is considered. The comparison of the solution against the published analytical results for the classic cases without bolts reinforcement is in good agreement for displacements as well as stresses. The solution is then applied to two real cases of face extrusion analysis of tunnel excavation in France and compared with both field measurements from the Tartaiguille tunnel and the extrusometer data as well as the three-dimensional (3D) calculation integrating face bolting reinforcement for the Toulon tunnel. The comparison of the results ensures full consistency of the solution in the predictive extrusion of the tunnel face and demonstrates, therefore, its efficacy and significant advantage in parametric analysis during the preliminary design stage.

An essential stage of mine design is an estimation of the steps of the first and periodic roof caving in longwall mines. Generally, this is carried out using the field experience and can be much enhanced by numerical simulation. In this work, the finite-difference method was applied coupled with the continuum damage mechanics (CDM) approach to simulate the stress-strain evolution of the rock mass with the underground opening during coal extraction. The steps and stages of roof caving were estimated relying on the numerical simulation data, and they were compared with the field data from several operating mines in the south of the Kuznetsk Basin, Russia. The dependence of the first roof caving step in simulation linearly correlates with field data. The results correspond to the actual roofs of longwall panels of the flat-dipping coal seams and the average rate of face advancement is approximately 5 m/day. Keywords: Longwall mining, Rock mass, Underground openings, Roof caving, Abutment pressure, Numerical simulation

Aeroelasticity studies the interaction between the aerodynamic loads and the flexible structures, and has gained much attention in the design of modern aircraft. Most of the existing computational fluid dynamics/computational structural dynamics (CFD/CSD) coupling approaches are based on Runge–Kutta method, central difference method, linear multi-step method and so on, which are conditionally stable and are unsuitable for the stiff problem that requires a very small time step to solve. In this paper, the precise integration method (PIM) formula is derived for the structural modal equations and then the PIM-based CFD/CSD coupling method is presented. The three-dimensional AGARD wing 445.6 and a sweptback wing are considered here for aeroelastic studies. The flutter results demonstrate that the presented method is comparable in accuracy to the traditional strong coupling method and has better numerical stability property than some exiting improved methods. For the static aeroelastic analyses, applying a large damping ratio to the structural equations helps to obtain the equilibrium quickly but may lead to the stiff problem, which was seldom discussed before. The results show that the presented PIM-based coupling method can overcome the stiff problem arising in static aeroelastic systems and is more efficient than the traditional coupling approach based on Runge–Kutta method, especially when a large damping ratio is applied.

In order to study the design of incomplete well point for groundwater extraction in open cut foundation pit in which the inner and outer aquifers are not completely isolated and the change mechanism of ground subsidence due to dewatering in the foundation pit, an open cut foundation pit for a subway station on Chengdu Metro Line 6 is taken as an example; meanwhile, the typical sandy pebble soil strata are also considered as a research object in this paper. Firstly, a new method for designing groundwater extraction in the open cut foundation pit is presented and applied to the practical project. The dewatering funnel curve is derived based on Dupuit’s assumption, and the ground subsidence around the foundation pit due to groundwater extraction is calculated using the stratification summation method as well as considering the effect of seepage force. The finite difference software FLAC3D is employed to simulate the groundwater extraction process in the foundation pit, and the simulation of groundwater extraction by single well point and group well points is also carried out and the unapparent effect of group well points is obtained. The comparison among on-site monitoring, theoretical calculation, and numerical simulation shows that these values have the same trend in indicating ground subsidence, and the conventional stratification summation method is conservative, and the algorithm considering the effect of seepage force is more accurate. Therefore, the ground subsidence curve caused by groundwater extraction in the foundation pit is presented. The above research methods and results can be applicable for practical engineering and be used to guide the design and construction of groundwater extraction in the foundation pit by using the open cut method in sandy pebble soil strata.

Due to the soil spatial variability, it is still challenging to quantify the long-term reliability of bridge pile foundations under scour conditions. In this paper, a life-cycle system reliability-based approach that can explicitly address the scour-hole geometry and stress history is presented. The finite difference models implemented with the modified load transfer curves are developed to predict the pile performance. Two serviceability failure modes, settlement failure and lateral deflection failure, are investigated in the reliability analysis. This developed approach provides a new tool for the long-term performance assessment and rehabilitation of bridge pile foundations.

Terzaghi’s consolidation theory assumes strain in soil due to applied overburden pressure is small, and permeability and thus the coefficient of consolidation (Cv) remain constant during c...

—A general method is presented for exciting discrete modes in waveguides of arbitrary geometry. Guided modes supported by the waveguide are first calculated using a finite difference frequency domain model. High efficiency holograms to excite these discrete modes are then generated using the Direct Search hologram generation algorithm. The Direct Search algorithm is optimised such that the inherent properties of waveguide modes are exploited to give faster execution times. A nodeless antiresonant photonic crystal fibre is considered as a test geometry, in which high-purity modes are experimentally excited and in-coupling efficiencies of up to 32.8% are obtained.

The static limit analysis of axially symmetric masonry domes subject to pseudo-static seismic forces is addressed. The stress state in the dome is represented by the shell stress resultants (normal-force tensor, bending-moment tensor, and shear-force vector) on the dome mid-surface. The classical differential equilibrium equations of shells are resorted to for imposing the equilibrium of the dome. Heyman’s assumptions of infinite compressive and vanishing tensile strength, alongside with cohesive-frictional shear response, are adopted for imposing the admissibility of the stress state. A finite difference method is proposed for the numerical discretization of the problem, based on the use of two staggered rectangular grids in the parameter space generating the dome mid-surface. The resulting discrete static limit analysis problem results to be a second-order cone programming problem, to be effectively solved by available convex optimization softwares. In addition to a convergence analysis, numerical simulations are presented, dealing with the parametric analysis of the collapse capacity under seismic forces of spherical and ogival domes with parameterized geometry. In particular, the influence that the shear response of masonry material and the distribution of horizontal forces along the height of the dome have on the collapse capacity is explored. The obtained results, that are new in the literature, show the computational merit of the proposed method, and quantitatively shed light on the seismic resistance of masonry domes.

One of important tasks in a development of gas-condensate fields is to minimize hydrocarbons loss arising from the gas condensation in pores of the gas-bearing layer. The search for the optimal gas production regime is carried out both on the basis of laboratory experiments and on the base of computer simulation. In this regard, the relevant is the verification of the constructed mathematical models by means of comparison of numerical results with experimental data obtained on the laboratory models of a hydrocarbon reservoirs. Within the classical approach on the basis of the Darcy law and the law continuity for flows, the model is formulated that describes the passing a multicomponent gas-condensate mixture through a porous medium in the depletion mode. The numerical solution of the corresponding system of nonlinear partial differential equations is implemented on the basis of the combined use of the C++ programming language and the Maple software. Shown that the approach used provides an agreement of results of numerical simulations with experimental data on the dynamics of hydrocarbon recoverability depending on the pressure obtained at VNIIGAZ, Ukhta.

Conventional window technologies tend to have poor thermal transmittance coefficients (U-values) which cause significant heat loss during the winter season and undesired heat gain in the summer. This study reports a new procedure to calculate center glass U-values of triple and quadruple windows which include low-emissive radiant energy veils – shades and blinds with spectrally selective coatings – between the outermost glass panes. A numerical zonal model is developed to simulate a net radiation system coupled with finite difference and ray tracing methods using validated derived experimental equations. A parametric investigation is carried out wherein the influence of different parameters such as optical properties, inter-pane distances and slat angles of the blinds on the thermal performance of the glazing system are analyzed. Three different gas fill types are examined under realistic boundary conditions. It is shown that this window system has a compelling U-value compared to ordinary multilayer glazing products.

A combination of finite difference and finite element methods was employed to develop a model for predicting the temperature development and thermally induced stresses in early-age concrete members (such as bridge footings, piers, columns, girders, and slabs). A two-dimensional finite difference (FD) scheme was utilized for heat generation and transfer within a hydrating concrete member. A finite element (FE) plane strain model was then established to compute the thermal stresses in the concrete subjected to the temperature changes. The FD-FE model can be easily created using any programing language, and the methodology can be used to predict the temperatures and stresses as well as assess the possibility of early-age cracking in concrete members.

The Poisson–Boltzmann equation (PBE) arises in various disciplines including biophysics, electrochemistry, and colloid chemistry, leading to the need for efficient and accurate simulations of PBE. However, most of the finite difference/element methods developed so far are rather complicated to implement. In this study, we develop a ResNet-based artificial neural network (ANN) to predict solutions of PBE. Our networks are robust with respect to the locations of charges and shapes of solvent–solute interfaces. To generate train and test sets, we have solved PBE using immersed finite element method (IFEM) proposed in (Kwon, I., Kwak, D. Y. Discontinuous bubble immersed finite element method for Poisson–Boltzmann equation. Communications in Computational Physics&nbsp, 2019, 25, pp. 928–946). Once the proposed ANNs are trained, one can predict solutions of PBE in almost real time by a simple substitution of information of charges/interfaces into the networks. Thus, our algorithms can be used effectively in various biomolecular simulations including ion-channeling simulations and calculations of diffusion-controlled enzyme reaction rate. The performance of the ANN is reported in the result section. The comparison between IFEM-generated solutions and network-generated solutions shows that root mean squared error are below 5·10−7. Additionally, blow-ups of electrostatic potentials near the singular charge region and abrupt decreases near the interfaces are represented in a reasonable way.

In the past few years, deep learning and its practical form of deep neural networks have been effectively used in a wide range of research areas. Researchers applied the deep learning techniques into solving Partial Differential Equations (PDEs) achieved significant results. A current approach known as Physics-Informed Neural Network (PINN), has evolved as a remarkable method to implement deep learning with the corresponding physics laws in forms of given linear or nonlinear PDEs. Using PINNs to solve PDEs can eliminate the requirements of elements grid needed in classical computational methods, such as finite difference or finite element methods. When approximating the solution of a PDE using a machine learning algorithm, it is vital to constrain the neural network to minimize the PDE residual. In this paper, a PINN architecture is presented, which employs the transient bioheat transfer equation (tBHTE) into a neural network to predict the temperature rise. The thermal model simulates the heat conduction generated from the wave propagating from ultrasound transducers. The solution of the tBHTE using PINNs utilizes a mesh-free domain while still maintaining a certain accuracy compared to conventional numerical methods. Further study of solving tBHTE with multi-elements ultrasound transducers can be generally applied to focused ultrasound treatments in order to predict the heat generation in more complex heterogeneous domains.

A steady-state non-isothermal process of forming a viscoelastic flat polymer film is considered. The polymer melt is extruded through a flat die, subjected to uniaxial stretching and at the same time air cooling, and then finally cooled down on a chill roll. It is assumed that the film is wide enough and the distance between the extruder die and the cooling roller is minimal to such an extent that the change in the width of a film in the course of longitudinal stretching can be neglected. From a rheological standpoint, a polymer melt is a viscoelastic fluid. The upper-convective Maxwell model is used, for which the viscosity and relaxation time are assumed to be temperature dependent. The mathematical model is supplemented by the equation of non-isothermal crystallization kinetics. The problem is solved by a numerical method of finite differences.

Remote photoplethysmography (rPPG) is a non-contact method to measure physiological signals, such as heart rate (HR) and respiratory rate (RR), from facial videos. In this paper, we constructed a central difference convolutional attention network with Huber loss to perform more robust remote physiological signal measurements. The proposed method consists of two key parts:1) Using central difference convolution to enhance the spatiotemporal representation, which can capture rich physiological related temporal context by gathering time difference information 2) Using Huber loss as the loss function, the gradient can be smoothly reduced as the loss value between the rPPG and ground truth PPG signal is closer to the minimum. Through experiments on multiple public datasets and cross-dataset evaluation, the good performance and robustness of the rPPG measurement network based on central difference convolution are verified.

Switched reluctance machines (SRMs) are getting more popular due to their uncomplicated and rugged structure. However, acoustic noise and vibration resemble two main issues with this type of machine. Radial forces acting on the machine stator contribute significantly to acoustic noise generation. These forces can be reduced by optimizing the machine geometry using deterministic optimization techniques. These techniques need the sensitivities of the cost function with respect to the design variables. In this work, the sensitivities of the radial force density components of SRMs are estimated with respect to various geometrical parameters using the adjoint variable method (AVM). The AVM method reduces the computational burden as compared to the more precise but computationally costly Central Finite Differences method (CFD).

Numerical integration of two-dimensional gradient data is an important step for many slope-measuring optical instruments. However, existing methods are limited by low accuracy or data location restrictions. The zonal integration algorithm in this paper is a generalized process that works with unordered data via Taylor series approximations of finite difference calculations. This method does not require iteration, and all significant steps rely on matrix calculations for a least-squares solution. Simultaneous integration and interpolation is achieved with high accuracy and arbitrary data locations.

This paper presents a set of new required programmes written in format data using the built-in programming FISH language available in three-dimensional Fast Lagrangian Analysis of Continua software (FLAC3D). These script data files were developed, to overcome difficulties noted during the nailed slope stability prediction. They established to analyse stability of general embankment slope cases under various soil nailing parameters design. To deal with 3D finite difference analysis results in terms of the factor of safety (FOS) and critical slip surface, both 2D finite difference and limit equilibrium (LEM) methods are also conducted. A comparison of the 3D and 2D results indicates that 2D analyses underestimate seriously stability predictions, notably in terms of the FOS. Therefore, it was concluded that, 3D analysis should be used as an alternative to the 2D analyses, even though it requires more time. Some useful conclusions are obtained from this work, which provides a good practice guidance for real life scenarios.