Numerical Approaches Research Articles

Seismic performance enhancement of underground structure influenced by CFRP wrapping schemes

The seismic failure mechanism of underground structures showing structural collapse is attributed to the deformation incompatibility between the central columns and the sidewalls, especially the insufficient deformation capacity of the central columns. Therefore, the approaches to improve the seismic performance of underground structures mainly aim at avoiding the damage of central columns. This paper presents a comparative study on the seismic performance of underground structures with the central columns retrofitted with different numbers of Carbon Fiber Reinforced Plastics (CFRP) layers. Seismic capacity of the CFRP retrofitting reinforced concrete (RC) columns was explored in detail through experimental and numerical approaches. Then numerical models were built and verified to simulate the behaviors of the CFRP retrofitting RC columns, and the seismic performance of the CFRP retrofitting underground structures was numerically simulated. Based on the numerical results, the damage of the CFRP retrofitting underground structures was calculated, and damage classification illustrated that the seismic performance of underground structures was enhanced remarkably. Finally, parametric studies were conducted to discuss about how the number of CFRP layers and the earthquake intensity affect the earthquake-induced damage of underground structures. Conclusions from this study could be referenced for seismic retrofitting of existing underground structures.

Effect of Vertical Location of Post-Opening on Seismic Behaviour of RC Shear Wall: Experimental and Numerical Analysis

The seismic performance of reinforced concrete (RC) shear walls with post-openings is critical in civil engineering. This study investigates the influence of post-opening positions on the seismic behaviour of RC shear walls through both experimental and numerical approaches. Four shear wall specimens with varying positions of post-openings were subjected to pseudo-static tests. Additionally, Finite Element Method (FEM) simulations were employed to further analyse the structural responses of shear walls with post-openings. The results show that the vertical position of post-openings significantly affects the failure mode, peak bearing capacity, and overall seismic performance. Peak bearing capacity reductions were observed, with central and bottom openings diminishing capacity by up to 17.5% and 15.1%, respectively, while top openings had a minimal impact. Openings also influenced pre-crack initiation, yielding behaviour, and stiffness degradation, with central openings causing the most significant effects. The ductility and energy dissipation capacities of the shear walls were also affected by opening positions. Bottom post-openings led to a maximum ductility reduction of 18.4%, while top openings increased ductility by up to 24.6%. Energy dissipation capacity decreased with lower post-opening locations, with central and bottom openings reducing capacity by 78.9% and 63.0%, respectively. These findings emphasize the importance of considering opening location in the seismic design of RC shear walls to optimize structural performance.

Puck 3D-based modeling and validation of progressive failure in instrumented glass fiber-reinforced polypropylene via the split-disk test

This study analyzes the mechanical behavior and damage progression of filament-wound thermoplastic composite rings, focusing on the effects of embedded fiber optic (FO) sensors. Utilizing a split-disk test, the study evaluates both experimental and numerical approaches to examine the impact of FO sensors in glass fiber-reinforced polypropylene composite rings. The split-disk test is employed to measure key mechanical properties such as hoop tensile strength, stiffness and failure strain using strain gauges and 3D Digital Image Correlation (DIC). The research specifically examines two extreme configurations of FO sensor placement: parallel and perpendicular to the reinforced fibers. The objective is to propose sensor integration that minimizes potential negative effects on the material's properties. Both instrumented and non-instrumented samples are analyzed numerically and experimentally. The experimental phase involves detailed mechanical characterization using the split-disk test, while the numerical approach uses a developed UMAT finite element model based on the 3D Puck failure criterion and an element weakening method for progressive failure analysis. The numerical models adopt real microstructural details according to optical microscopic analysis. The study concludes that parallel embedded FO sensors are preferable as they enhance the ultimate strength to failure and avoid creating resin-rich zones near the sensor, thereby improving the overall mechanical performance of the composite rings. The 3D Puck failure criterion combined with the element weakening method provides accurate predictions of fiber failure initiation and growth in the composite rings.

Comprehensive investigation of gas hold-up in a double coaxial mixer with shear-thinning fluids exhibiting yield stress: Experimental, numerical, and artificial neural network approaches

This study addresses the challenge of uneven gas dispersion in yield-stress, non-Newtonian fluids, commonly encountered in industries such as biopharmaceuticals, cosmetics, and food processing. While previous research demonstrated the advantages of dual coaxial mixers for pseudoplastic fluids, limited attention has been given to aerating yield-pseudoplastic fluids with higher aspect ratios. This study bridges that gap by investigating both local and global gas hold-up under various conditions, utilizing electrical resistance tomography and computational fluid dynamics. Key findings showed that increasing the anchor speed from stationary to 30 rpm significantly enhanced aeration efficiency (gas hold-up per specific power consumption), with improvements of 78 % in UP-CO mode and 25 % in UP-COUNTER mode at Nc = 350 rpm and Qg = 20 L/min. These results underscore enhanced gas dispersion under specific operating conditions, driving overall process intensification. To ensure accurate prediction of gas hold-up, both dimensional and dimensionless empirical correlations, along with an artificial neural networks (ANNs) model, were developed. The ANNs model exhibited superior accuracy, achieving R² values of 0.99 for both rotation modes, outperforming empirical models, which achieved R² values of 0.90 and 0.89 for UP-CO and UP-COUNTER modes, respectively.

Effective elastic properties of 3D lattice materials with intrinsic stresses: Bottom-up spectral characterization and constitutive programming

Analytical investigations to characterize the effective mechanical properties of lattice materials allow an in-depth exploration of the parameter space efficiently following an insightful, yet elegant framework. 2D lattice materials, which have been extensively dealt with in the literature following analytical as well as numerical and experimental approaches, have limitations concerning multi-directional stiffness and Poisson's ratio tunability. The primary objective of this paper is to develop mechanics-based formulations for a more complex analysis of 3D lattices, leading to a physically insightful analytical approach capable of accounting the beam-level mechanics of pre-existing intrinsic stresses along with their interaction with 3D unit cell architecture. We have investigated the in-plane and out-of-plane effective elastic properties to portray the physics behind the deformation of 3D lattices under externally applied far-field normal and shear stresses. The considered effect of beam-level intrinsic stresses therein can be regarded as a consequence of inevitable temperature variation, pre-stress during fabrication, inelastic and non-uniform deformation, manufacturing irregularities etc. Such effects can notably impact the effective elastic properties of lattice materials, quantifying which for 3D honeycombs is the central focus of this work. Further, from the material innovation viewpoint, the intrinsic stresses can be deliberately introduced to expand the microstructural design space for effective elastic property modulation of 3D lattices. This will lead to programming of effective properties as a function of intrinsic stresses without altering the microstructural geometry and lattice density. We have proposed a generic spectral framework of analyzing 3D lattices analytically, wherein the beam-level stiffness matrix including the effect of bending, axial, shear and twisting deformations along with intrinsic stresses can be coupled with the unit cell mechanics for obtaining the effective elastic properties.

CFD Evaluation of Respiratory Particle Dispersion and Associated Infection Risk in a Coach Bus with Different Ventilation Configurations

The COVID-19 pandemic has underscored the urgency of understanding virus transmission dynamics, particularly in indoor environments characterized by high occupancy and suboptimal ventilation systems. Airborne transmission, recognized by the World Health Organization (WHO), poses a significant risk, influenced by various factors, including contact duration, individual susceptibility, and environmental conditions. Respiratory particles play a pivotal role in viral spread, remaining suspended in the air for varying durations and distances. Experimental studies provide insights into particle dispersion characteristics, especially in indoor environments where ventilation systems may be inadequate. However, experimental challenges necessitate complementary numerical modeling approaches. Zero-dimensional models offer simplified estimations but lack spatial and temporal resolution, whereas Computational Fluid Dynamics, particularly with the Discrete Phase Model, overcomes these limitations by simulating airflow and particle dispersion comprehensively. This paper employs CFD-DPM to simulate airflow and particle dispersion in a coach bus, offering insights into virus transmission dynamics. This study evaluates the COVID-19 risk of infection for vulnerable individuals sharing space with an infected passenger and investigates the efficacy of personal ventilation in reducing infection risk. Indeed, the CFD simulations revealed the crucial role of ventilation systems in reducing COVID-19 transmission risk within coach buses: increasing clean airflow rate and implementing personal ventilation significantly decreased particle concentration. Overall, infection risk was negligible for scenarios involving only breathing but significant for prolonged exposure to a speaking infected individual. The findings contribute to understanding infection risk in public transportation, emphasizing the need for optimal ventilation strategies to ensure passenger safety and mitigate virus transmission.

Performance Evaluation of RC Structures using Next- Generation Performance-Based Seismic Assessment Procedures

Seismic forces have wreaked havoc on buildings around the world, resulting in both property damage and human deaths. Reinforced concrete structures under cyclic loading cannot be predicted using current methods, according to relevant design codes. Code-based seismic design procedures have been replaced by performance-based design procedures (PBSD). PBSD describes a building's overall performance by taking into account its structural and non-structural performance categories. Immediate occupancy, life safety, and collapse prevention are the three types of damage that can be encountered in a construction site. They are ranked based on the amount of damage, downtime, and casualties they inflict. Although these procedures can detect damage, they are unable to assign a numerical value to the seriousness of the damage. The use of damage indices, which are based on structural and response-based parameters, has been proposed by many researchers in the past. The objective of current research is an attempt to summarise all of these efforts and identify grey areas for further investigation. Numerical approaches to integrate structural damages with various PBSD performance levels have been proposed.

Mechanical Properties of Two-Dimensional Metal Nitrides: Numerical Simulation Study.

It is expected that two-dimensional (2D) metal nitrides (MNs) consisting of the 13th group elements of the periodic table and nitrogen, namely aluminium nitride (AlN), gallium nitride (GaN), indium nitride (InN) and thallium nitride (TlN), have enhanced physical and mechanical properties due to the honeycomb, graphene-like atomic arrangement characteristic of these compounds. The basis for the correct design and improved performance of nanodevices and complex structures based on 2D MNs from the 13th group is an understanding of the mechanical response of their components. In this context, a comparative study to determine the elastic properties of metal nitride nanosheets was carried out making use of the nanoscale continuum modelling (or molecular structural mechanics) method. The differences in the elastic properties (surface shear and Young's moduli and Poisson's ratio) found for the 2D 13th group MNs are attributed to the bond length of the respective hexagonal lattice of their diatomic nanostructure. The outcomes obtained contribute to a benchmark in the evaluation of the mechanical properties of AlN, GaN, InN and TlN monolayers using analytical and numerical approaches.

Temperature and rate dependent shear characterization and modeling of spread-tow woven Flax/PP composite laminates

This paper investigates the in-plane shear behavior of spread-tow woven structured flax fiber-reinforced polypropylene composites, focusing on temperature and displacement rate effects. For this aim, the study includes bias-extension experiments to characterize the shear behavior of the material. Several experiments were conducted at different displacement rates and temperature levels. The temperature levels were chosen to encompass the material's behavior during solid and molten-state thermoforming, given the melting and decomposition temperatures acquired from differential scanning calorimetry and thermogravimetric analysis tests, respectively. A new fixture was designed and manufactured to allow pre-heating of the oven and rapid placement of the samples, which in turn, prevents their degradation for the time duration required to reach a uniform temperature distribution in the oven. During the experiments, the 3D digital image correlation technique accurately measured local deformations and strains on the specimen's surface under varying conditions. Further, a finite element model is developed, incorporating a fiber reorientation algorithm with a hypo-elastic shear model to simulate the material's temperature and rate-dependent behavior. The finite element shear angle distributions, as well as the shear angle-force and shear angle-displacement curves, are compared with the Digital Image Correlation (DIC) data and load measurements for different test conditions, showing good agreement between the numerical and experimental approaches.

Solutions to SIR/SEIR epidemic models with exponential series: Numerical and non numerical approaches

This study revisits the mathematical SIR/SEIR epidemic models, aiming to introduce novel exponential-type series solutions. Beyond standard non-dimensionalization, we implement a successful rescaling technique that reduces the parameter count in classical epidemiology. Consequently, solutions for the SIR model are determined solely by the basic reproduction number and initial infected fractions. Similarly, the SEIR model requires only the transmission-to-recovery ratio and initial exposed fractions. We present both numerical and non numerical solutions, alongside elucidating the limitations on the existence of exponential-type series solutions. Our analysis reveals that these solutions are valid under two key conditions: endemic situations and early epidemic stages, where the basic reproduction number is close to one. We graphically illustrate the range of physical parameters guaranteeing the existence of non numerical exponential series solutions. However, for epidemic/pandemic outbreaks with significantly higher reproduction numbers, achieving complete convergence of the exponential series across the entire physical domain becomes impossible. In such cases, we divide the exponential series solution into two zones: from initial time to peak time and from peak time to the final epidemic time. For the first zone, where convergence is slow, we successfully employ Padé approximants to accelerate the convergence of the series. This accelerated solution is then smoothly joined to the second zone solution once the peak time is identified within the first region. The presented non numerical solutions are envisioned to serve as valuable benchmarks for testing and enhancing other numerical approaches used to solve epidemic models and their variants.

A Review of Simulation Tools for Thin-Film Solar Cells.

Unlike current silicon-based photovoltaic technology, the development of last-generation thin-film solar cells has been marked by groundbreaking advancements in new materials and novel structures to increase performance and lower costs. However, physically building each new proposal to evaluate the device's efficiency can involve unnecessary effort and time. Numerical simulation tools provide a solution by allowing researchers to predict and optimize solar cell performance without physical testing. This paper reviews thirteen of the main numerical simulation tools for thin-film solar cells, including SCAPS, AMPS, AFORS-HET, ASPIN3, GPVDM, SESAME, SILVACO, SENTAURUS, and ADEPT. This review evaluates each tool's features, modeling methods, numerical approaches, and application contexts. The findings reveal notable differences in material modeling, numerical accuracy, cost, and accessibility among the tools. Each tool's strengths and limitations in simulating thin-film solar cells are highlighted. This study emphasizes the necessity of selecting suitable simulation tools based on specific research requirements. It provides a comparative analysis to assist researchers in choosing the most effective software for optimizing thin-film solar cells, contributing to advancements in photovoltaic technology.

Determination of the REV size for heterogeneous rocks with different grain sizes: Deep learning and numerical approaches

Accurate determination of the representative elementary volume (REV) size plays a pivotal role in analysing the mechanical properties and failure processes of heterogeneous rocks in complex engineering environments. In this study, a novel microstructure modelling strategy (NMMS) for determining the REV size is proposed by combining deep learning and an improved phase-field method (PFM). Micro- and macroscale experiments are systematically conducted to determine the real microstructural characteristics and mechanical properties of heterogeneous rocks with different grain sizes. On the basis of this experimental evidence, geometric models of different sizes were reconstructed through deep learning to avoid the limitations of human-based methods, and an improved PFM was used for numerical calculations. These models were then employed to perform numerical tests under uniaxial loading conditions, and the coefficient of variation was introduced to determine the REV size of heterogeneous rocks with different grain sizes. The research findings indicate that the final REV size is the maximum value of the REVs defined by the evaluation properties within an acceptable coefficient of variation. At a criterion of 5% for the coefficient of variation, the REV sizes are 60 mm×60 mm, 70 mm×70 mm, and 90 mm×90 mm for fine-medium-grained (FMG), medium-grained (MG), and coarse-grained (CG) rocks, respectively. Furthermore, the REV determined by the NMMS was applied to investigate the effects of microstructure on macromechanical properties and damage evolution under triaxial loading conditions. The numerical results show that the NMMS can accurately predict the macromechanical properties and microcracking patterns of heterogeneous rocks, especially the intracrystalline cracks in feldspar, the interfacial cracks in gravel, and the “voids” of cracks in biotite. This research can provide some basic references for the optimal choice of the REV size of heterogeneous rocks.

Novel conformal structure-preserving schemes for the linearly damped nonlinear Schrödinger equation

In this work, by utilizing the Strang splitting technique, some advanced conformal structure-preserving schemes are developed for solving the damped nonlinear Schrödinger equation (DNLSE). The proposed innovative numerical approaches, namely the high-order compact conformal multi-symplectic method and the conformal momentum-preserving method, have two key computational advantages. Firstly, these two approaches excel in conserving local structures, and more importantly, they are capable of maintaining exact energy dissipation rates in any time-space region, particularly under periodic boundary conditions. To validate the theoretical properties and demonstrate the efficacy and stability of these approaches in long-time integrations, we conduct through extensive numerical simulations involving both bright and dark solitons.

Differential quadrature lattice Boltzmann method for simulating fluid flows

In this study, a novel method for simulating incompressible flows using the lattice Boltzmann method is presented, aiming to improve robustness. This method is enhanced by the Qadyan numerical method. In the Qadyan method, Partial differential equations are solved using semi-discrete schemes combined with the differential quadrature method. To discretize the spatial derivatives of the lattice Boltzmann equation, the upwind differential quadrature method is employed, while the first-order forward difference scheme and/or fourth-order Runge-Kutta method handle the temporal term. The decision to exclude more complex methods stems from their requirement for refined computational grids. This work focuses on achievable results with similar types of uniform grids. The proposed scheme introduces and evaluates a novel method for solving both steady and unsteady problems. The present numerical method is validated by solving five benchmark problems, including heat diffusion on a slab, Stokes’ first problem, Taylor-Green vortex flow, flow around a flat plate, and flow in a lid-driven cavity. Reasonable agreements are obtained between the solutions obtained using this method and those from analytical/other numerical approaches. The Qadyan formulation delivers more accurate results compared to the finite-difference lattice Boltzmann method, (FDLBM), without requiring an increase in the number of grids. Notably, the novel Qadyan method achieves this increased accuracy without introducing additional complexity to the standard lattice Boltzmann method or resorting to non-uniform grids. This is possible due to the nature of the differential quadrature method, which utilizes more combinations of candidate stencils. The Qadyan method has a higher computational cost in comparison with the FDLBM.

Groundwater-surface water exchanges in an alluvial plain in southern France subjected to pumping: A coupled multitracer and modeling approach

Study regionThe study was conducted in an alluvial plain between the Rhône and the Ouvèze Rivers (in the southeast of France) extensively exploited for drinking water. The research area is characterized by significant groundwater-surface interactions influenced by groundwater pumping activities. Study focusThe aim of this study is to enhance the understanding of interactions between rivers and alluvial aquifers by combined multi-tracer and numerical modeling approaches. Over an 18-month period, groundwater temperature, piezometric levels, and river surface water levels were continuously monitored. Field campaigns focused on conductivity, stable isotopes of water, and radon-222 activity concentration in both groundwater and surface water. Radon-222 was used to quantify water exchanges between the river and the aquifer. A MODFLOW model, calibrated using piezometric data and PEST, was employed to simulate groundwater flow and reactive transport of radon-222 using MT3DMS. New hydrological insights for the regionThe study reveals that river water recharges the aquifer, with radon-222 data delineating this recharge zone. The methodology extended the interpretation of periodic groundwater temperature signals to isotopic signals, allowing the identification of dispersivity and Darcy's velocity. The Ouvèze River was found to contribute approximately 55 % of the pumping water supply, alongside the Rhône. These findings provide valuable insights for sustainable water resource management, demonstrating the relevance of using natural tracers in scenarios where artificial tracers are impractical.

Numerical Simulation of SEIR Model for COVID-19 Infection

One of the most basic models in epidemiology, the SEIR (Susceptible-Exposed-Infectious-Recovered) model explains how viral infections spread through communities. This study analyzes the SEIR model's differential equations to learn more about its dynamic behaviors. This study discusses the 2019 corona virus disease (COVID-19) epidemic model using numerical methods of susceptible exposed infected recovered (SEIR). A numerical description of the notion is provided using two numerical approaches, including forward Euler and RK-4 approaches. The subplots of SEIR model are drawn by ode 45 commands. The stability of disease free equilibrium and Endemic equilibrium points are depicted. The significance of comprehending the interaction between epidemiological variables and population dynamics in developing efficient public health treatments is brought to light in this study, which investigates the consequences of these equations on the transmission and management of infectious diseases. Insights into the dynamics of illness transmission and potential measures for mitigating its effects are presented through the use of mathematical analysis and computational simulations. Jagannath University Journal of Science, Volume 11, Number 1, June 2024, pp. 172−185

Comparative analysis of buoyancy-driven hydromagnetic flow and heat transfer in a partially heated square enclosure using Cu-Fe3O4 and MoS2-Fe3O4 nanofluids

Purpose This study aims to investigate entropy generation through natural convection and examine heat transfer properties within a partially heated and cooled enclosure influenced by an angled magnetic field. The enclosure, subjected to consistent heat production or absorption, contains a porous medium saturated with a hybrid nanofluid blend of Cu-Fe3O4 and MoS2-Fe3O4. Design/methodology/approach The temperature and velocity equations are converted to a dimensionless form using suitable non-dimensional quantities, adhering to the imposed constraints. To solve these transformed dimensionless equations, the finite-difference method, based on the MAC (Marker and Cell) technique, is used. Comprehensive numerical simulations address various control parameters, including nanoparticle volume fraction, Rayleigh number, heat source or sink, Darcy number, Hartmann number and slit position. The results are illustrated through streamlines, isotherms, average Nusselt numbers and entropy generation plots, offering a clear visualization of the impact of these parameters across different scenarios. Findings Results obtained show that the Cu-Fe3O4 hybrid nanofluid exhibits higher entropy generation than the MoS2-Fe3O4 hybrid nanofluid when comparing them at a Rayleigh number of 106 and a Darcy number of 10–1. The MoS2 hybrid nanofluid demonstrates a low permeability, as evidenced by an average Darcy number of 10–3, in comparison to the Cu hybrid nanofluid. The isothermal contours for a Rayleigh number of 104are positioned parallel to the vertical walls. Additionally, the quantity of each isotherm contour adjacent to the hot wall is being monitored. The Cu and MoS2 nanoparticles exhibit the highest average entropy generation at a Rayleigh number of 105 and a Darcy number of 10–1, respectively. When a uniform heat sink is present, the temperature gradient in the central part of the cavity decreases. In contrast, the absence of a heat source or sink leads to a more intense temperature distribution within the cavity. This differs significantly from the scenario where a uniform heat sink regulates the temperature. Originality/value The originality of this study is to examine the generation of entropy in natural convection within a partially heated and cooled enclosure that contains hybrid nanofluids. Partially heated corners are essential for optimizing heat transfer in a wide range of industrial applications. This enhancement is achieved by increasing the surface area, which improves convective heat transfer. These diverse applications encompass fields such as chemical engineering, mechanical engineering, surface research, energy production and heat recovery processes. Researchers have been working on improving the precision of heated and cold corners using various methods, such as numerical, experimental and analytical approaches. These efforts aim to enhance the broad utility of these corners further.

Perbandingan Integrasi Numerik Metode Simpson Tiga per Delapan dan Romberg Menggunakan Pemrograman Perl Hypertext Prepocessor

Difficult integral problems that cannot be solved analytically often require numerical approaches. PHP (Perl Hypertexr Prepocessor) programming has become one of the tools that can be used to solve numerical problems. This research aims to develop a numerical integration program using the Simpson 3/8 method and Romberg method on polynomial, exponential, and trigonometric functions with PHP programming, as well as to compare the efficiency of both methods based on relative error and execution time. Based on the implementation of the algorithms of both methods in PHP programming, the research results show that the average error for the Simpson 3/8 method and Romberg method are 0,013787% and 0,001356%, respectively. The comparison of errors between these two methods indicates that the Romberg method is 9,89% more accurate than the Simpson 3/8 method. However, in terms of program execution time, the Simpson 3/8 method requires less time compared to the Romberg method. The average execution time for the Simpson 3/8 method and Romberg method are 0,00117 seconds and 1,77811 seconds, respectively, and the comparison of execution time between these two methods shows that the Simpson 3/8 method is shorter than the Romberg method when using the same number of iterations.

Damage analysis and assessment of concrete T-girder bridge based on fire scene numerical reconstruction

Fire is a sporadic disaster of concrete bridges, with diverse fire environments and complex damage mechanisms. Accurately evaluating the damage situation of concrete bridges after a fire is exceedingly challenging. This study formulates a damage analysis and assessment method based on the step-by-step and progressively deepening working principle. The method relies on fire scene numerical reconstruction and encompasses key technical aspects, including bridge detection and analysis during the fire incident, fire scene numerical reconstruction, and subsequent bridge damage assessment. Building upon these principles, the study utilizes results from the detection and analysis of the concrete T-girder bridge during a fire incident to establish Computational Fluid Dynamics (CFD) and Finite Element Method (FEM) models for the numerical reconstruction of the fire scene. These models enable the calculation of varying temperature distributions and the evolution of the bridge under fire. Compared with the parameters obtained through the ISO834 method, the numerical reconstruction approaches not only enhances the accuracy of replicating the bridge combustion process but also enables the extraction of temperature field distribution patterns within the bridge fire space and its concrete components.

Transfer Learning-Based Physics-Informed Convolutional Neural Network for Simulating Flow in Porous Media with Time-Varying Controls

A physics-informed convolutional neural network (PICNN) is proposed to simulate two-phase flow in porous media with time-varying well controls. While most PICNNs in the existing literature worked on parameter-to-state mapping, our proposed network parameterizes the solutions with time-varying controls to establish a control-to-state regression. Firstly, a finite volume scheme is adopted to discretize flow equations and formulate a loss function that respects mass conservation laws. Neumann boundary conditions are seamlessly incorporated into the semi-discretized equations so no additional loss term is needed. The network architecture comprises two parallel U-Net structures, with network inputs being well controls and outputs being the system states (e.g., oil pressure and water saturation). To capture the time-dependent relationship between inputs and outputs, the network is well designed to mimic discretized state-space equations. We train the network progressively for every time step, enabling it to simultaneously predict oil pressure and water saturation at each timestep. After training the network for one timestep, we leverage transfer learning techniques to expedite the training process for a subsequent time step. The proposed model is used to simulate oil–water porous flow scenarios with varying reservoir model dimensionality, and aspects including computation efficiency and accuracy are compared against corresponding numerical approaches. The comparison with numerical methods demonstrates that a PICNN is highly efficient yet preserves decent accuracy.