Value Of Time Step Research Articles

Improvement of Relative DEM Time Step Range in Fast Fluidization Simulation of Type-A FCC Particles

In many process engineering fields, gas-particle fluidized beds are widely used. In fluidized bed research, the discrete element method, or DEM, has been a powerful tool for design and operation purposes. However, with the use of Type-A powders, fluid catalytic cracking or FCC particles being classical cases, they have hardly been reported in DEM simulations of fast fluidization. This study paid close attention to the suitable selection of a stiffness constant and a DEM time step. To reflect their respective effects and complicated interactions, a so-called relative DEM time step was defined. The drag coefficient was correlated using the energy-minimization multi-scale (EMMS) approach to reasonably calculate the gas–solid interaction. Six representative cases with different relative time step values were chosen to simulate a micro-fluidized bed of Type-A FCC powders. The results showed that DEM employing EMMS-based drag force was able to greatly enlarge the suitable range of relative time steps in a fast fluidization simulation of Type-A powders. In addition, the typical macro flow structures of fast fluidization was successfully captured: axially dilute in the top and dense in the bottom, and radially dilute in the core and dense near the wall. Moreover, the distinct gas–solid backmixing, which is considered one of the most important pieces of evidence for the determination of fast fluidization regimes, was modeled. It was indicated that the EMMS-based drag model attenuated the overestimated drag force so that the soft-sphere contact model would be able to more appropriately deal with particle collision, and thus improve the suitable relative DEM time step range.

A truly-explicit time-marching formulation for elastodynamic analyses considering locally-adaptive time-integration parameters and time-step values

In this paper, a novel explicit time-marching procedure, which adapts to the properties of the spatially discretized model, is discussed for the time-domain solution of elastodynamic problems. The proposed technique is entirely automated and highly effective, providing a very attractive formulation to analyse complex wave propagation models. The novel approach is second-order accurate, truly explicit, truly self-starting, and it enables adaptive algorithmic dissipation and extended stability limits. In addition, automated subdomain/sub-cycling splitting procedures may also be carried out in the analyses, enhancing the performance of the proposed formulation. In this context, the technique automatically divides the domain of the model into multiple subdomains (according to the properties of the discretized problem), in which different time-step values are applied, still guaranteeing stability and enabling more accurate and efficient analyses. Adaptive values for the time-integration parameters of the method, which are established following the elements of the adopted spatial discretization, are also considered, providing a locally-defined self-adjustable formulation. This approach allows creating a link between the applied spatial and temporal solution procedures, enabling their errors to be better counterbalanced. Expressions for the adaptive time-integration parameters of the method and for the limiting time-step values of the elements of the discretized domain are presented and discussed. At the end of the paper, benchmark analyses are performed to demonstrate the effectiveness of the proposed technique, considering illustrative theoretical problems and applied intricate models, which are equivalent to those of real applications in the OIL & GAS industry.

Higher-order implicit shock-capturing scheme based on linearization of implicit fluxes for the Euler equations

PurposeA higher-order implicit shock-capturing scheme is presented for the Euler equations based on time linearization of the implicit flux vector rather than the residual vector.Design/methodology/approachThe flux vector is linearized through a truncated Taylor-series expansion whose leading-order implicit term is an inner product of the flux Jacobian and the vector of differences between the current and previous time step values of conserved variables. The implicit conserved-variable difference vector is evaluated at cell faces by using the reconstructed states at the left and right sides of a cell face and projecting the difference between the left and right states onto the right eigenvectors. Flux linearization also facilitates the construction of implicit schemes with higher-order spatial accuracy (up to third order in the present study). To enhance the diagonal dominance of the coefficient matrix and thereby increase the implicitness of the scheme, wave strengths at cell faces are expressed as the inner product of the inverse of the right eigenvector matrix and the difference in the right and left reconstructed states at a cell face.FindingsThe accuracy of the implicit algorithm at Courant–Friedrichs–Lewy (CFL) numbers greater than unity is demonstrated for a number of test cases comprising one-dimensional (1-D) Sod’s shock tube, quasi 1-D steady flow through a converging-diverging nozzle, and two-dimensional (2-D) supersonic flow over a compression corner and an expansion corner.Practical implicationsThe algorithm has the advantage that it does not entail spatial derivatives of flux Jacobian so that the implicit flux can be readily evaluated using Roe’s approximate Jacobian. As a result, this approach readily facilitates the construction of implicit schemes with high-order spatial accuracy such as Roe-MUSCL.Originality/valueA novel finite-volume-based higher-order implicit shock-capturing scheme was developed that uses time linearization of fluxes at cell interfaces.

Forecasting Short-Term Passenger Flow of Subway Stations Based on the Temporal Pattern Attention Mechanism and the Long Short-Term Memory Network

Rational use of urban underground space (UUS) and public transportation transfer underground can solve urban traffic problems. Accurate short-term prediction of passenger flow can ensure the efficient, safe, and comfortable operation of subway stations. However, complex and nonlinear interdependencies between time steps and time series complicate such predictions. This study considered temporal patterns across multiple time steps and selected relevant information on short-term passenger flow for prediction. A hybrid model based on the temporal pattern attention (TPA) mechanism and the long short-term memory (LSTM) network was developed (i.e., TPA-LSTM) for predicting the future number of passengers in subway stations. The TPA mechanism focuses on the hidden layer output values of different time steps in history and of the current time as well as correlates these output values to improve the accuracy of the model. The card swiping data from the Hangzhou Metro automatic fare collection system in China were used for verification and analysis. This model was compared with a convolutional neural network (CNN), LSTM, and CNN-LSTM. The results showed that the TPA-LSTM outperformed the other models with good applicability and accuracy. This study provides a theoretical basis for the pre-allocation of subway resources to avoid subway station crowding and stampede accidents.

NON-POLYNOMIAL CUBIC SPLINE APPROACH FOR NUMERICAL APPROXIMATION OF SECOND ORDER LINEAR KLEIN-GORDON EQUATION

Most of the fundamental theories and mathematical models of engineering and physical sciences are expressed in terms of partial differential equations (PDEs). Several studies were carried out for the numerical approximation of the second order linear Klein-Gordon equation. This study constructed a new numerical technique for the numerical approximation of second order linear Klein-Gordon equation. The new constructed scheme was based on employing non-polynomial cubic spline method (NPCSM). The second order time derivatives involved in the linear Klein-Gordon equation were decomposed into the first order derivatives. The decomposition generated a linear system of PDEs, where the first order time derivatives were approximated by the central finite differences of . Three test problems were considered for the numerical illustration of the developed scheme. For different values of spatial displacement , step size , and time step , the developed numerical technique produced encouraging results which were very much close to the analytical solution. For , , and , the best observed accuracy was close to the machine precision.

DEEP REINFORCEMENT LEARNING WITH HIDDEN MARKOV MODEL FOR SPEECH RECOGNITION

Nowadays, many applications uses speech recognition especially the field of computer science and electronics, Speech Recognition (SR) is the interpretation of words spoken into a text. It is also known as Speech-To-Text (STT) or Automatic-Speech-Recognition(ASR), or just Word-Recognition(WR). The Hidden-Markov-Model (HMM) is a type of Markov model, which means that the future state of the model depends on the current state, not on the entire history of the system and the goal of HMM is to learn a sequence of hidden states from a set of known states. The Long-Short-Time-Memory (LSTM) network is a type of Recurrent Neural Network (RNN) that can learn long-term dependencies between time steps of sequence data. The LSTM network is trained by the network in order to predict the values of subsequent time steps in a series-to-series regression. Deep Neural Network (DNN) models are better classifiers than Gaussian Mixture Models (GMMs), they can generalize much better with a smaller number of parameters over complex distributions. They model distributions of different classes jointly, called “distributed” learning, or, more properly “tied” learning. This work is aimed at developing a speech recognition model that will predict isolated speech of some selected fruits in Hausa, Igbo and Yoruba language by using the predicting power of Mel-Frequency-Cepstral-Coefficient (MFCC), LSTM and HMM algorithms. The findings of the study would improve the development of better automatic speech applications systems and would benefit the academic and research community in the field of Natural Language Processing.

Avaliação de sistema de captação de água de chuva através de simulação contínua com dados subdiários

ABSTRACT A rainwater harvesting system, designed for non-potable water uses, can be helpful for runoff generation control. To evaluate this, sub-daily time steps for monitoring and continuous simulations are important tools. Therefore, this paper shows a performance assessment of a rainwater harvesting system for both roof runoff control (maximum flow rate and drained volume) and to meet water demand, from data obtained in a monitoring apparatus and also from continuous simulation using 1-minute time steps data. The model SWMM was calibrated and validated for both a roof and a monitoring apparatus during the monitored period 2018-2019. Thereafter, continuous simulations were accomplished using rainfall, evaporation, and demand time series. For this stage, data satisfied nearly seven years (2014-2020) containing one-minute time step values. Results have shown the control is influenced by the combined action of the first-flush diverter and rainfall regime and was shown to be greater at maximum flow rate than volume.

Integrated and Individual Impacts of Land Use Land Cover and Climate Changes on Hydrological Flows over Birr River Watershed, Abbay Basin, Ethiopia

Land use/land cover (LULC) and climate change are the two major environmental factors that affect water resource planning and management at different scales. This study aims to investigate the effects of LULC and climate change patterns for a better understanding of the hydrological processes of the Birr River watershed. To examine the effects of LULC and climate change patterns on hydrology, three periods of climate data (1986–1996, 1997–2007 and 2008–2018) and three sets of LULC maps (1986, 2001 and 2018) were established. The changes in hydrological flow caused by climate and LULC changes were estimated using the soil and water assessment tool (SWAT) and indicator of hydrological alteration (IHA) method. Results showed that the SWAT model performed well during the calibration and validation period at monthly timestep, with R2 and NSE values of (0.83 and 0.81) and (0.80 and 0.71), respectively. The LULC change increased surface runoff while decreasing baseflow, water yield, and evapotranspiration. This was due to increased agriculture and settlements, and a reduction in bushland, forest, and grassland. Climate change increased surface runoff and water yield while decreasing baseflow and evapotranspiration during 1996–2006. The combined effect of LULC and climate reveals increased surface runoff and a decreased trend of evapotranspiration, whereas baseflow and water yield showed inconsistency. In addition, the IHA found no statistically significant increasing trend for one-day, three-days, seven-day, and thirty-day minimum and maximum daily streamflow in the Birr River watershed. These findings will be useful to authorities, water engineers, and managers concerned with hydrology, LULC, and climate.

Development of a Stable Implicit Method Without Numerical Dissipation for Nonlinear Structural Dynamic Analysis

This paper develops a self-starting implicit time integration method for nonlinear dynamic analysis. The method is single-step and is based on a non-dissipative second-order accurate approximation scheme. The method employs simple expressions for velocity and acceleration while internal forces are calculated at a specified point. This point results from a weighted combination of the relevant displacements and velocities at the bounds of the time step. In the linear case, the scheme is unconditionally stable, there is no amplitude decay for any time step value and the period elongation is the same as in the Newmark scheme. In nonlinear case, the scheme maintains the same numerical characteristics of dissipation and dispersion of the Newmark scheme while demonstrating a substantial improvement in stability. Summarizing, the presented scheme (i) is a single-step scheme with self-starting attribute; (ii) does not involve additional variables or artificial parameters chosen by the user; (iii) has at least second-order accuracy; (iv) shows to have very wide stability ranges in nonlinear analyses. It also proves that the computational effort per step required by the presented scheme is the same as the effort required in the widely used implicit single-step methods and a substantial reduction in the number of Newton–Raphson iterations in the steps is obtained. For comparison, methods with similar characteristics such as Newmark, generalized-[Formula: see text] and Bathe schemes are tested. Stiff nonlinear problems regarding elastic behavior and finite element structural models are analyzed to compare the considered solution methods.

Parametric research on the time step and spring stiffness in three‐dimensional discontinuous deformation analysis method

AbstractThree‐dimensional discontinuous deformation analysis method (3D.DDA) is a dynamic calculation method based on the implicit solution. Inertial force is introduced in the solution process to ensure that the time variable is the real time variable, and springs are applied at the block boundary to avoid mutual intrusion between blocks. Therefore, the value of time step and contact spring stiffness directly affect the accuracy of 3D.DDA calculation results. Firstly, we analyzed the effects of the time step and contact spring stiffness on the numerical calculation results of the 3D.DDA method based on the theoretical formula derivation. Secondly, we studied the influence mechanism of time step on the simulation results of the 3D.DDA method individually based on the double block free falling model. And we determined the reasonable value area of time step. Then, considering the contacts between blocks, we studied the joint influence mechanism of time step and contact spring stiffness on the 3D.DDA simulation results based on the double block sliding model. And we analyzed the error between the 3D.DDA simulation value and the theoretical value under the conditions of different time step and contact spring stiffness. Based on that, we divided the combined value area of time step and contact spring stiffness into four regions (Q1, Q2, Q3, and Q4) and determined the optimal value area of time step and contact spring stiffness. At last, we carried out the slope rockfall model experiment and numerical simulation, and the trajectory of the falling rock in the numerical simulation was basically consistent with the experiment results, which verified the effectiveness of the optimal value area of time step and contact spring stiffness. The research results can provide a reference for the choice of the value of time step and contact spring stiffness in the numerical simulation based on the 3D.DDA method.

An improved adaptive formulation for explicit analyses of wave propagation models considering locally-defined self-adjustable time-integration parameters

In this paper, a novel explicit time-marching procedure is proposed for wave propagation analyses, considering an improved adaptive formulation. In this adaptive approach, different time-integration parameters are defined for each element of the adopted spatial discretization, allowing different stability limits (as well as other properties) to be locally applied. Thus, self-adjustable dissipative and non-dissipative parameters are automatically distributed along the discretized domain of the model, following the properties of its elements, and their use is triggered regarding the behaviour of the computed responses. In this context, the errors of the adopted spatial discretization method may be properly countervailed by the time-integration procedure, allowing substantially better accuracy to be provided. In addition, as is discussed along the manuscript, the novel time-marching formulation is very simple to implement and to apply, and it provides more efficient analyses than standard time integration techniques, enabling larger time-step values to be considered as well as reduced computational efforts to be attained per time step. At the end of the paper, numerical results are presented, illustrating the effectiveness and excellent performance of the proposed technique.

Improved algorithm for a system with different stiffness for positive and negative displacements

In the process of investigation of dynamics of elements of robots, systems with different values of stiffness for positive and negative displacements play an important role. This change of the value of stiffness has an effect to the results of numerical calculation of dynamics of the system. For more precise investigation of dynamics a special numerical procedure is proposed in the paper. Numerical results for two values of time steps: large and medium ones, are presented for two cases: without application of the proposed procedure and with application of it. Comparison of the presented results indicates advantages of the proposed numerical procedure.

An application of the scale-adapted simulation to the unsteady flow across a tube bundle

In the last decades, one of the main objectives pursued in the field of computational fluid dynamics has been the development of turbulent flow models and simulations techniques capable of generating predictions of flow patterns accurate enough to many industrial applications in a reasonable wall-clock time and at an acceptable cost. Very often, a trade-off has to be sought between the engineer’s expectations regarding the accuracy of the model and the limited computational resources available. In that framework, the present contribution aims at demonstrating the capabilities of the SST-SAS approach which is considered as an intermediate model with respect to accuracy and computational requirements. To that end, the turbulent flow through a tube bundle was selected as test case. Preliminary sensitivity analyses were carried out to properly choose the residuals tolerance level, duration of the physical time integration, mesh size and time step value. The SST-SAS results are compared with available experimental data as well as with different simulations results taken from the literature. A quantitative scoring criterion was defined to sort out the different models results: the SST-SAS was at the top, sharing the first place with a URANS-RSM approach.

Automated Particle Tracing & Sensitivity Analysis for Residence Time in a Saturated Subsurface Media

Residence time of water flow is an important factor in subsurface media to determine the fate of environmental toxins and the metabolic rates in the ecotone between the surface stream and groundwater. Both numerical and lab-based experimentation can be used to estimate the residence time. However, due to high variability in material composition in subsurface media, a pragmatic model set up in the laboratory to trace particles is strenuous. Nevertheless, the selection and inclusion of input parameters, execution of the simulation, and generation of results as well as post-processing of the outcomes of a simulation take a considerable amount of time. To address these challenges, an automated particle tracing method is developed where the numerical model, i.e., flow and reactive transport code, MIN3P, and MATLAB code for tracing particles in saturated porous media, is used. A rectangular model domain is set up considering a fully saturated subsurface media under steady-state conditions in MIN3P. Streamlines and residence times of the particles are computed with a variety of seeding locations covering the whole model surface. Sensitivity analysis for residence time is performed over the varying spatial discretization and computational time steps. Moreover, a comparative study of the outcomes with Paraview is undertaken to validate the automated model (R2 = 0.997). The outcome of the automated process illustrates that the computed residence times are highly dependent on the accuracy of the integration method, the value of the computational time step, ∆t, spatial discretization, stopping criterion for the integration process of streamlines, location, and amount of seed points. The automated process can be highly beneficial in obtaining insights into subsurface flow dynamics with high variability in the model setup instead of laboratory-based experimentation in a computationally efficient manner.

Analyzing melting process of paraffin through the heat storage with honeycomb configuration utilizing nanoparticles

To intensify the charging rate of thermal storage, new honeycomb configuration has been utilized in this work. The various material were utilized for solid structure namely: Stainless steel (SS); Aluminum-6061-T4 (Al-6061) and pure aluminum (Al). The holes were filled with mixture of paraffin (RT82) and Al2O3 nanoparticles. To create various configurations of holes with honeycomb shape, the geometric factor (b2) has three levels and another geometric factor was calculated to reach the equal volume of paraffin in all geometries. Characteristics of NEPCM were measured based on homogeneous model. The two dimensional laminar melting process was simulated based on finite volume approach. The size of mesh and value of time step have been optimized to decrease the computing price and precision of code was tested with matching the data with exist published article. With decrease of b2, the thickness of honeycomb reduces and number of holes increases. When b2 = 1 mm, the required time decreases around 90.87% and 24.28% with changing the material from SS to Al and Al-6061. With utilize of Al, the melting time decreases around 27.96% with reduce of b2. The lowest period is about 6.548 min which belongs to case with pure aluminum and b2 = 1 mm.

Numerical Simulation for One-Dimensional (1D) Wave Propagation by Solving the Shallow Water Equations using the Preissmann Implicit Scheme

This research simulated one-dimensional wave propagation by solving the shallow water equations using the Preissman implicit numerical scheme due to its ability to maintain simplicity and stability at a larger time step value. This numerical model was fundamentally developed to satisfy the shallow water condition, where the water depth or horizontal-length scale is much smaller than the free-surface disturbance wavelength or vertical-length scale, and to comprehensively test the accuracy of the model. Consequently, three different types of waves were considered and these include (1) tidal, (2) roll, and (3) solitary. In the first case, the model was proven to be robust and accurate due to its relatively-small errors for both water-surface elevation and velocity indicating that the Preismann scheme is suitable for longwave simulations. In the second case, it was fairly accurate in capturing the periodic permanent roll waves despite showing a higher water-surface elevation than the one observed and this discrepancy is due to the neglect of the turbulent Reynold stress in the model. Meanwhile, the last case showed remarkable discrepancies in the water-surface elevation because the dispersion effect is quite significant during the wave propagation. This indicates that the Preismann scheme underestimated the wave crest along with time when the dispersion term was neglected. All simulations were performed using the tridiagonal matrix algorithm, thereby eliminating the need for iterations for the solution of the Preismann scheme. The findings of this study are beneficial to the next generation of the Preissmann-scheme models which can be designed to include turbulence and dispersion terms.

A Fast Mean-Preserving Spline for Interpolating Interval Data

Abstract Interpolation of interval data where the mean is preserved, e.g., estimating smoothed, pseudodaily meteorological variables based on monthly means, is a common problem in the geosciences. Existing methods for mean-preserving interpolation are computationally intensive and/or do not readily accommodate bounded interpolation, where the interpolated data cannot exceed a threshold value. Here we present a mean-preserving, continuous, easily implementable, and computationally efficient method for interpolating one-dimensional interval data. Our new algorithm provides a straightforward solution to the interpolation problem by utilizing Hermite cubic splines and midinterval control points to interpolate interval data into smaller partitions. We further include adjustment schemes to restrict the interpolated result to user-specified minimum and maximum bounds. Our method is fast, portable, and broadly applicable to a range of geoscientific data, including interpolating unbounded time series such as mean temperature, and bounded data including mean wind speed or cloud-cover fraction. Significance Statement Interpolation is often utilized to mathematically estimate smaller time step values when such data are not readily available, for example, the estimation of daily temperature when only monthly temperature values are available. We propose a novel interpolation method based on linking segments of flexible continuous curves that ensures the average of interpolated result will be the same as the original value, which is important for minimizing interpolation errors. We find that our new method takes significantly less computational time when compared with other existing methods, while retaining a similar degree of precision. Furthermore, we outline an additional procedure for users to specify the minimum and maximum bounds of interpolated results if applicable.

Modeling neighborhood-scale shallow geothermal energy utilization: a case study in Berlin

Nowadays, utilizing shallow geothermal energy for heating and cooling buildings has received increased interest in the building sector. Among different technologies, large borehole heat exchanger arrays are widely employed to supply heat to various types of buildings. Recently, a 16-borehole array was constructed to extract shallow geothermal energy to provide heat to a newly-developed public building in Berlin. To guarantee the quality of the numerical model and reveal its sensitivity to different subsurface conditions, model simulations were conducted for 25 years with two finite element simulators, namely the open-source code OpenGeoSys and the widely applied commercial software FEFLOW. Given proper numerical settings, the simulation results from OpenGeoSys and FEFLOW are in good agreement. However, further analysis reveals differences with respect to borehole inflow temperature calculation implemented in the two software. It is found that FEFLOW intrinsically uses the outflow temperature from the previous time step to determine the current inflow temperature, which makes it capable of much faster simulation by avoiding iterations within a single time step. In comparison, OpenGeoSys always updates the inflow and outflow temperature based on their current time step values. Because the updates are performed after each iteration, it delivers more accurate results with the expense of longer simulation time. Based on this case study, OpenGeoSys is a valid alternative to FEFLOW for modeling ground source heat pump systems. For modellers working in this field, it is thus recommended to adopt small enough time step size, so that potential numerical error can be avoided.

Application of long short-term memory recurrent neural networks for localisation of leak source using 3D computational fluid dynamics

Gas leaks represent a major concern in industrial sites due to potential human and economical losses. Prompt identification of leak scenarios favours corrective maintenance avoiding the domino effect. In this paper, long short-term memory recurrent neural networks were trained and tested to CH4 leakage source in a chemical process module. We exploit the benefits of varying the temporal length of input variables, and the datasets were obtained employing 3D-CFD simulations. We consider four leak locations, four wind speeds, and eight wind directions, besides the non-leakage scenario for the same wind speeds and directions. The models were trained using different values of timesteps to evaluate the prediction accuracy for unseen data. Results showed progressive improvement of the performance of the models with greater values of timesteps, and good generalisation with test accuracy over 95.3%, indicating the ability of the model to correctly predict the leakage source using easily monitored variables.

A Semi-Analytical Solution Approach for Solving Constant-Coefficient First-Order Partial Differential Equations

Simulation and control of many dynamic systems involve solving partial differential equations (PDE). This letter proposes a semi-analytical solution (SAS) approach for fast and high-quality solution of first-order PDEs. The region of interest of the studied PDE is divided into a grid, and an SAS is derived for each grid cell in the form of the multivariate polynomials, of which the coefficients are identified using initial value and boundary value conditions. The solutions are solved in a “time-stepping” manner, i.e., within one time step, the coefficients of the SAS are identified and the initial value of the next time step is evaluated. This approach achieves a significantly larger grid cell than the widely used finite difference method, and thus enhances the computational efficiency significantly. The simulation result on the natural gas pipeline model demonstrates the advantages of SAS in accuracy and computational efficiency.