Stochastic Numerical Approach Research Articles

A stochastic numerical approach on the diagonal shear behavior of brick masonry wallettes fabricated with traditional lime-sand mortar

A stochastic numerical approach on the diagonal shear behavior of brick masonry wallettes fabricated with traditional lime-sand mortar

Numerical investigation of heat and mass transfer in micropolar nanofluid flows over an inclined surface with stochastic numerical approach

Numerical investigation of heat and mass transfer in micropolar nanofluid flows over an inclined surface with stochastic numerical approach

A Stochastic Numerical Approach to Study Stagnation Point Carreau Nanofluid Flow Impacted by Thermal Radiation and Activation Energy

A Stochastic Numerical Approach to Study Stagnation Point Carreau Nanofluid Flow Impacted by Thermal Radiation and Activation Energy

Application of Machine Learning Coupled with Stochastic Numerical Analyses for Sizing Hybrid Surge Vessels on Low-Head Pumping Mains

In surge protection, low-head profiles are deemed a challenge in pump failure events since they are prone to severe negative pressure surges that require an uneconomical surge vessel volume. A hybrid surge vessel with a dipping tube can provide required protection with reasonable economic volume. This work presents novel analyses for the hybrid surge vessel and develops a simple model for its optimum sizing using a stochastic numerical approach coupled with machine learning. Practical ranges for correct sizing of vessel components, such as ventilation tube, inlet/outlet air valves, and compression chamber, are presented for optimal protection and performance. The water hammer equations are iteratively solved using the hybrid surge vessel’s revised boundary conditions within the method of characteristics numerical framework to generate 2000 cases representing real pump failures on low-head pipelines. Genetic programming is utilized to develop simple relations for prediction of the hybrid vessel initial and expanded air volumes in addition to the compression chamber volume. Moreover, the developed model presented a classification index for low-head pipelines on which the hybrid vessel would be most economical. The developed model yielded good prediction error statistics. The developed model proves to be more accurate and easier to use than the classical design charts for the low-head pumping mains. The model clearly showed the relation between various hydraulic and pipe parameters, with pipe diameter and static head as the most influencing parameters on compression chamber volume and expanded air volume. The developed model, together with the classification indices, can be used for preliminary surge protection sizing for low-head pipelines.

A stochastic numerical approach for a class of singular singularly perturbed system.

In the present study, a neuro-evolutionary scheme is presented for solving a class of singular singularly perturbed boundary value problems (SSP-BVPs) by manipulating the strength of feed-forward artificial neural networks (ANNs), global search particle swarm optimization (PSO) and local search interior-point algorithm (IPA), i.e., ANNs-PSO-IPA. An error-based fitness function is designed using the differential form of the SSP-BVPs and its boundary conditions. The optimization of this fitness function is performed by using the computing capabilities of ANNs-PSO-IPA. Four cases of two SSP systems are tested to confirm the performance of the suggested ANNs-PSO-IPA. The correctness of the scheme is observed by using the comparison of the proposed and the exact solutions. The performance indices through different statistical operators are also provided to solve the SSP-BVPs using the proposed ANNs-PSO-IPA. Moreover, the reliability of the scheme is observed by taking hundred independent executions and different statistical performances have been provided for solving the SSP-BVPs to check the convergence, robustness and accuracy.

A Numerical Study of the Fractional Order Dynamical Nonlinear Susceptible Infected and Quarantine Differential Model Using the Stochastic Numerical Approach

The theme of this study is to present the impacts and importance of the fractional order derivatives of the susceptible, infected and quarantine (SIQ) model based on the coronavirus with the lockdown effects. The purpose of these investigations is to achieve more accuracy with the use of fractional derivatives in the SIQ model. The integer, nonlinear mathematical SIQ system with the lockdown effects is also provided in this study. The lockdown effects are categorized into the dynamics of the susceptible, infective and quarantine, generally known as SIQ mathematical system. The fractional order SIQ mathematical system has never been presented before, nor solved by using the strength of the stochastic solvers. The stochastic solvers based on the Levenberg-Marquardt backpropagation scheme (LMBS) along with the neural networks (NNs), i.e., LMBS-NNs have been implemented to solve the fractional order SIQ mathematical system. Three cases using different values of the fractional order have been provided to solve the fractional order SIQ mathematical model. The data to present the numerical solutions of the fractional order SIQ mathematical model is selected as 80% for training and 10% for both testing and validation. For the correctness of the LMBS-NNs, the obtained numerical results have been compared with the reference solutions through the Adams–Bashforth–Moulton based numerical solver. In order to authenticate the competence, consistency, validity, capability and exactness of the LMB-NNs, the numerical performances using the state transitions (STs), regression, correlation, mean square error (MSE) and error histograms (EHs) are also provided.

Falkner–Skan Equation with Heat Transfer: A New Stochastic Numerical Approach

In this study, a new computing model is developed using the strength of feedforward neural networks with the Levenberg–Marquardt method- (NN-BLMM-) based backpropagation technique. It is used to find a solution for the nonlinear system obtained from the governing equations of Falkner–Skan with heat transfer (FSE-HT). Moreover, the partial differential equations (PDEs) for the unsteady squeezing flow of heat and mass transfer of the viscous fluid are converted into ordinary differential equations (ODEs) with the help of similarity transformation. A dataset for the proposed NN-BLMM-based model is generated in different scenarios by a variation of various embedding parameters, Deborah number ( β ) and Prandtl number (Pr). The training (TR), testing (TS), and validation (VD) of the NN-BLMM model are evaluated in the generated scenarios to compare the obtained results with the reference results. For the fluidic system convergence analysis, a number of metrics such as the mean square error (MSE), error histogram (EH), and regression (RG) plots are utilized for measuring the effectiveness and performance of the NN-BLMM infrastructure model. The experiments showed that comparisons between the results of the proposed model and the reference results match in terms of convergence up to E-05 to E-10. This proves the validity of the NN-BLMM model. Furthermore, the results demonstrated that there is an increase in the velocity profile and a decrease in the thickness of the thermal boundary layer by increasing the Deborah number. Also, the thickness of the thermal boundary layer is decreased by increasing the Prandtl number.

Heat transfer between two porous parallel plates of steady nano fludis with Brownian and Thermophoretic effects: A new stochastic numerical approach

The design of integrated numerical computing through back-propagated neural networks with Levenberg-Marquard system (BNN-LMS) is presented to explore the fluid mechanics problems governing the system of heat transfer between two porous parallel plates of steady nanofluids (HTPSNF) under the stimulus of thermophoretic and Brownian motion. By introducing the similarity transformations, the original system model HTPSNF in terms of PDEs is converted to nonlinear ODEs. Strength of Homotopy Analysis Method (HAM) is utilized the governing equations of original model HTPSNF to obtain the data set. Reference collection for the suggest BNN-LMS scheme is originated in terms of various scenarios associated HTPSNF such as Porosity parameter, Schmidt number, Brownian parameter, viscosity parameter, Prandlt number and thermophoric parameter. To uphold the trueness of the suggest BNN-LMS, the validation, training and testing process of BNN-LMS are accomplished to govern the estimate solution of HTPSNF for various cases and evaluation with reference results. The comparative studies and performance analyses based on outcomes of MSE, error histograms, correlation and regression intimate the effectiveness and virtue of designed LMBNN technique. Mean Square Errors in the ranges of 10−07 to 10−14 confirm the perfection of the presented methodology for the closed correspondence between suggested and reference results.

Stochastic numerical technique for solving HIV infection model of CD4+ T cells

The intension of the present work is to present the stochastic numerical approach for solving human immunodeficiency virus (HIV) infection model of cluster of differentiation 4 of T-cells, i.e., CD4+ T cells. A reliable integrated intelligent computing framework using layered structure of neural network with different neurons and their optimization with efficacy of global search by genetic algorithms supported with rapid local search methodology of active-set method, i.e., hybrid of GA-ASM, is used for solving the HIV infection model of CD4+ T cells. A comparison between the present results for different neurons-based models and the numerical values of the Runge–Kutta method reveals that the present intelligent computing techniques is trustworthy, convergent and robust. Statistics-based observation on different performance indices further demonstrates the applicability, effectiveness and convergence of the present schemes.

Stochastic numerical approach for solving second order nonlinear singular functional differential equation

A new computational intelligence numerical scheme is presented for the solution of second order nonlinear singular functional differential equations (FDEs) using artificial neural networks (ANNs), global operator genetic algorithms (GAs), efficient local operator interior-point algorithm (IPA), and the hybrid combination of GA-IPA. An unsupervised error function is assembled for the DDE optimized by ANNs using the hybrid combination of GA-IPA. Three kinds of the second order nonlinear singular DDEs have been solved numerically and compared their results with the exact solutions to authenticate the performance and exactness of the present designed scheme. Moreover, statistical analysis based on Mean absolute deviation, Theil's inequality coefficient and Nash Sutcliffe efficiency is also performed to validate the convergence and accuracy of the present scheme.

On the Modeling of Acrylic Acid Copolymerization in an Aqueous Solution: A Modular, Integrated Approach

A complete mathematical model of the free‐radical copolymerization of acrylic acid in an aqueous solution, taking place in a pilot‐scale tubular reactor equipped with static mixers, is presented. The developed kinetic/reactor model is numerically integrated in terms of a coupled deterministic–stochastic numerical approach that combines the advantages of speed, efficiency, and increased predictive capabilities. A series of experimental measurements on the monomer conversion and the molecular weight characteristics of the produced copolymer, under a wide range of process conditions, are used for the identification of the kinetic model parameters while a thorough analysis of the compositional characteristics of the produced copolymers is also carried out in terms of a series of bivariate distributed properties. image

Consistent Behavior of Eulerian Monte Carlo fields at Low Reynolds Numbers

A slightly different version of the Eulerian Monte Carlo method (EMC) (Valino, Flow Turbul. Combust. 60, 157–172, (1998)) is presented in this paper. The EMC method is an effective stochastic numerical approach to solve the Probability Density Function (PDF) of reacting species in turbulent flows. In contrast with the original formulation, the spurious Wiener term associated with the molecular diffusion is removed, by splitting the micro-mixing into mean gradient and fluctuating contributions. The evolution of the EMC fields representing the PDF in the proposed formulation is then consistent in the laminar limit: the EMC fields follow the same standard convection-diffusion equation, without any stochastic terms.

On the uncertainty quantification of the unsteady aerodynamics of 2D free falling plates

The aim of this paper is to conduct a statistical analysis of the effects of the fillet radii on the dynamics of the falling plate using the nonintrusive spectral projection (NISP) method. The free fall of two-dimensional cards immersed in a fluid was studied using a deterministic and stochastic numerical approach. The motion is characterized by the fluid-body interaction described by coupling the Navier–Stokes and rigid body dynamic equations. The model’s predictions have been validated using both experimental and numerical data available in the literature. In the stochastic simulations, the fillet radius of the plate was considered a random variable characterized by a uniform probability density function introducing, in this way, some uncertainties in the plate’s trajectory. To take into account the uncertainties, we employed the NISP method based on polynomial chaos expansion. The analysis was focused on finding the ensemble mean trajectory and error bar for a confidence interval of 95 % for both tumbling and fluttering regimes.

Characterization of Fracture Network System of the Midale Field

Abstract Enhanced oil recovery from challenging/complex fields requires extensive analysis of reservoir structure and good understanding of the effect of this structure on the dynamics of the process. Naturally fractured reservoirs are good examples of this kind and their fracture network characterization is still a bigchallenge. In this study, we analyzed the fracture network system of a portion of the Midale Field, a naturally fractured carbonate reservoir in the Williston Basin of southeastern Saskatchewan, Canada. Our study aims at an extensive characterization of fracture and fracture network properties and construction of a reliable fracture network model for further use in assessing the oil recovery by CO2 injection and CO2 sequestration potential. We integrated static data such as cores, logs and well tests to build 3D discrete fracture network models. Stochastic numerical approach was applied using a commercial software package. A fracture network constructed from static data was calibrated using well test data. Several parameters were evaluated in sensitivity studies to determine those characteristics of the network which have higher influence on the reservoir performance. Simulated well test response was checked against previously published well test data. This study allowed us to recognize uncertainties in critical parameters and propose some measures to manage those uncertainties. Introduction The Midale is a carbonate field located in southeastern Saskatchewan. Following the discovery in 1953, the field was developed on 32 ha spacing and proved to bear 81.9 ? 106 Sm3 reserves of 28.7 °API oil. The field belongs to the Mississippian oil trend located along the northern margin of Williston Basin. Subsequent to primary production up to 1962, the field was subjected to waterflooding on 83 inverted nine-spot patterns. To maintain the production which declined after 1964, an intensive program of vertical and horizontal infill drilling was undertaken. As of the end of 2006, approximately 1,000 wells exist in the field and more than 25% of OOIP was produced with an average watercut of 92%(1). The Midale Field is currently being subjected to tertiary recovery by miscible CO2 flooding. This field-scale CO2 injection was preceded by a 1.78 ha pilot project in 1984 ? 1989 which paved the way for a larger demonstration project. The CO2 Flood Demonstration Project encompassed 10% of the Midale Unit and paved the way for the field-scale application, which is expected to end up with an incremental recovery of 15% of OOIP(2). The Midale Field does not meet typical screening criteria for CO2 flooding. Nevertheless, extensive research and field applications proved that a proper design based on the analyses of the special combination of petrophysical, lithological and fracturing data can result in a successful carbon dioxide flood. The 24 m thick Midale Reservoir section consists of two main layers: dolomite-dominated "Marly" and vugular limestone, called "Vuggy". Both strata contain systematic fractures, though the degree of fracturing varies. Numerous studies conducted on the field revealed some characteristics of the natural fracture network (NFN) by both inverse methods, such as waterflood and carbon dioxide flood performance analyses, and well test analyses and direct methods such as core and log analyses.

Modelling spatial patterns of vegetation in desert sand dunes

A stochastic numerical approach was developed to model the actual standing biomass in the sand dunes of the northwestern Negev (Israel) and probable boundary conditions that may be responsible for the vegetation patterns investigated in detail. Our results for several variables characteristic for the prevailing climate, geomorphology, hydrology and biologicy at four measurement stations along a transect from northwest to southeast allowed for the development of a stochastic model for biomass distribution over the entire sand dune field (mesoscale) and at Nizzana experimental station (microscale). With this equation it was possible to compute and interpolate a biomass index value for each grid point on the mesoscale and micro scale. The spatial distribution of biomass is negatively linked to distance from the sea, to rainfall and relief energy.

Theory and simulations of squeeze-out dynamics in boundary lubrication

The dynamics of expulsion of the last liquidlike monolayer of molecules confined between two surfaces (measured recently for the first time [J. Chem. Phys. 114, 1831 (2001)]) has been analyzed by solving the two-dimensional Navier–Stokes equation combined with kinetic Monte Carlo simulations. Instabilities in the boundary line of the expelled film produce a rough boundary for all length scales above a critical value. The squeeze-out of liquid is shown to result from the 2D-pressure gradient in the lubrication film in the contact area. The Monte Carlo simulations agrees well with experiments, reproducing most qualitative and quantitative features. In particular it shows the formation of small islands, which (in the absence of pinning mechanism) drift slowly to the periphery of the contact area. We calculate the drift velocity analytically as a function of the distance of the island to the periphery of the contact area. Experiments indicate that some kind of pinning mechanism prevails, trapping fluid pockets for very long times. When including such pinning areas in the simulations, three distinct squeeze phases and time scales were observed: (1) initial fast squeeze of most of the fluid; (2) slower squeeze of unpinned fluid pockets; (3) long term pinning of fluid pockets. We also show that a distribution of small pinning areas may produce a synergistic effect, slowing down the second phase of the squeeze, compared to a small number of big pinning areas. The paper presents a new stochastic numerical approach to problems of moving boundaries which naturally accounts for thermal fluctuations and their effect in unstable dynamics.

The stochastic modeling of solidification structures in alloy 718 remelt ingots

A stochastic numerical approach was developed to model the formation of grain structure and secondary phases during the solidification of nickel-based alloy 718 remelt ingots. The significance of the present stochastic approach is that the simulated phases can be directly compared with actual phases from experiments at two different scales: grain characteristics can be visualized at the macroscale, while the amount, size, and distribution of secondary phases can be viewed at the microscale. The computer becomes a “dynamic metallographic microscope.” Stochastic modeling was applied to simulate the formation of solidification phases (γprimary phase and NbC and eutectic γ-Laves secondary phases) during the solidification of vacuum-arc-remelted and electroslag-remelted alloy 718 ingots. Modeling results, such as pool profile, grain-growth pattern, grain structure (both columnar and equiaxed grains), columnar-to-equiaxed transition, grain size, and secondary dendrite arm spacing, as well as amount, size, and location of both eutectic γ-Laves and NbC phases compared well with experimental data for cast alloy 718. This research demonstrates that the stochastic approaches are relatively fast, comprehensive, and more accurate than the deterministic approaches in predicting the solidification characteristics of remelt ingots and are mature enough to be used effectively by the metal industry for process development and optimization.