Numerical Techniques Research Articles

Breach Analysis of Earthen Dam

Failure of a levee or dam breach can result in severe economic losses and loss of human life. To minimize these consequences, it's imperative to assess the risks associated with levee breaches. This involves accurately predicting the volume of water released during a breach and simulating the propagation of flood waves across the floodplain to create inundation maps. Despite extensive observation and research into representing dam breaches and deriving crucial breach parameters like width, height, and side slope, there is no universally accepted method for determining these parameters. This study aims to evaluate existing methodologies for dam breach analyses, highlighting their advantages, limitations, and the challenges that lie ahead in this field. Earthen dams play a crucial role in water resource management and flood control. However, breaches in these structures pose significant risks to surrounding communities and infrastructure. This study explores the causes of earthen dam breaches, focusing on hydraulic, geotechnical, and structural factors. Through a comprehensive analysis of historical case studies and numerical modeling techniques, we elucidate the underlying mechanisms leading to dam failures. Furthermore, this research investigates effective mitigation strategies to enhance the resilience of earthen dams against breach incidents. By identifying key vulnerabilities and implementing targeted interventions, we aim to minimize the likelihood and impact of future breaches, ensuring the safety and sustainability of earthen dam infrastructure. Keywords— Breach analysis; Geotechnical Engineering; Earthen dam and Gangapur Dam

Dynamic characteristics of density-graded cellular materials for impact mitigation

Due to their exceptional impact resistance capabilities, density-graded cellular materials have immense potential in applications where crashworthiness requirements are of prime importance. Under impact loading, the deformation in these materials is characterized by compaction front propagation. Previous studies have utilized numerical techniques to solve the equations governing compaction shock propagation for cellular materials with density gradation. In this study, analytical solutions are formulated using compaction front position as the independent variable. The expressions for the velocity of the impinging rigid mass, energy absorption, incident stress, and transmitted stress are determined. The analytical solutions are shown to be in excellent agreement with the cell-based finite element solutions. The effect of density gradient on energy absorption and stresses is studied. The impact resistance factor is employed to assess different density-graded cellular materials for their effectiveness in impact mitigation. This study demonstrates that density-graded cellular materials can offer superior impact protection to objects at both the incident and transmitted ends. Lower density toward the incident end enhances impact resistance to objects located there, and likewise, lower density at the transmitted end offers more impact resistance to objects at that end.

Air–Water Two-Phase Flow Dynamics Analysis in Complex U-Bend Systems through Numerical Modeling

This study aims to provide insights into the intricate interactions between gas and liquid phases within flow components, which are pivotal in various industrial sectors such as nuclear reactors, oil and gas pipelines, and thermal management systems. Employing the Eulerian–Eulerian approach, our computational model incorporates interphase relations, including drag and non-drag forces, to analyze phase distribution and velocities within a complex U-bend system. Comprising two horizontal-to-vertical bends and one vertical 180-degree elbow, the U-bend system’s behavior concerning bend geometry and airflow rates is scrutinized, highlighting their significant impact on multiphase flow dynamics. The study not only presents a detailed exposition of the numerical modeling techniques tailored for this complex geometry but also discusses the results obtained. Detailed analyses of local void fraction and phase velocities for each phase are provided. Furthermore, experimental validation enhances the reliability of our computational findings, with close agreement observed between computational and experimental results. Overall, the study underscores the efficacy of the Eulerian approach with interphase relations in capturing the complex behavior of the multiphase flow in U-bend systems, offering valuable insights for hydraulic system design and optimization in industrial applications.

Comparison of Single-Phase Mathematical Models for Solid-State Packed Beds for Thermal Energy Storage

This article presents an analytical solution for the evaluation of the thermal performance of packed bed sensible heat storage. The numerical model developed was tested for four different solid storage mediums. The thermal energy equation is solved numerically by deploying the finite difference method. The presented analytical solution is based on a novel mathematical approach. The numerical model was validated using the computer simulation package Comsol Multiphysics v5.3. Our numerical model results are in good agreement with the published experimental data, with an overall difference of ~10%. Hence, the numerical model is an efficient way of evaluating the thermal performance of packed bed thermal energy storage systems compared to other numerical strategies or computer simulation techniques. This proves that the novel analytical model has shown to be a reliable and broadly accurate approach to acquire the thermal performance of sensible heat storage.

A Numerical Study of the Effect of Water Speed on the Melting Process of Phase Change Materials Inside a Vertical Cylindrical Container

The present work offers a thorough analysis of the impact of water velocity on phase change material (PCM) melting in a vertical cylindrical container. A detailed quantitative analysis uses sophisticated numerical techniques, namely the ANSYS/FLUENT 16 program, to clarify the complex relationship between enthalpy and porosity during the melting process. The experimental focus is on phase transition materials based on paraffin wax, particularly Rubitherm RT42. This study’s primary goal is to evaluate the effects of different water velocities (that is, at velocities of 0.01 m/s, 0.1 m/s, and 1 m/s) on the PCM’s melting behavior at a constant temperature of 333 K. This work intends to make a substantial contribution to the development of thermal energy storage systems by investigating new perspectives on PCM behavior under various flow circumstances. The study’s key findings highlight the possible ramifications for improving PCM-based thermal energy storage devices by revealing significant differences in melting rates and behavior that correlate to changes in water velocities. Future research is recommended to explore the impact of temperature variations, container geometries, and experimental validation to improve the accuracy and practicality of the results and to advance the creation of sustainable and effective energy storage solutions.

The Method of Finite Averages: A rigorous upscaling methodology for heterogeneous porous media

Rigorous upscaling techniques offer accurate and computationally-efficient strategies for modeling the average behaviors of multi-physical, multiscale phenomena in geological porous media. However, such techniques often rely on a variety of methodological assumptions that prohibit their rigorous application to practical systems (e.g., systems involving heterogeneous porous media, system-scale boundary conditions, and fine-scale dynamics that are not diffusion-dominant). In this work, we aim to formulate an upscaling methodology with few methodological assumptions to provide high levels of model generality and foster the utilization of rigorously-derived upscaled models in practice. In particular, we introduce the Method of Finite Averages (MoFA), a novel upscaling methodology for rigorously modeling heterogeneous porous media and system-scale boundary conditions. We detail MoFA’s implementation for the advective–diffusive transport of a single species and compare the methodology with classic numerical techniques, as well as other rigorous upscaling techniques, to highlight MoFA’s unique combination of rigor and generality. We then validate the derived model while demonstrating its benefits in three numerical experiments. The results suggest that (1.) the applicability and a priori error guarantees of MoFA models do not directly depend on system geometry, (2.) a model’s applicability and error guarantees can be can arbitrarily expanded and reduced, respectively, with further computational expense, and (3.) downscaling with MoFA provides an efficient strategy for generating accurate pore-scale solutions from upscaled results. Ultimately, the results evidence that upscaled models can be rigorously derived for heterogeneous porous media systems and resolved in a fraction of the time it takes to perform the equivalent pore-scale simulations.

Ex vivo, in vivo and in silico studies of corneal biomechanics: a systematic review.

Healthy cornea guarantees the refractive power of the eye and the protection of the inner components, but injury, trauma or pathology may impair the tissue shape and/or structural organization and therefore its material properties, compromising its functionality in the ocular visual process. It turns out that biomechanical research assumes an essential role in analysing the morphology and biomechanical response of the cornea, preventing pathology occurrence, and improving/optimising treatments. In this review, ex vivo, in vivo and in silico methods for the corneal mechanical characterization are reported. Experimental techniques are distinct in testing mode (e.g., tensile, inflation tests), samples' species (human or animal), shape and condition (e.g., healthy, treated), preservation methods, setup and test protocol (e.g., preconditioning, strain rate). The meaningful results reported in the pertinent literature are discussed, analysing differences, key features and weaknesses of the methodologies adopted. In addition, numerical techniques based on the finite element method are reported, incorporating the essential steps for the development of corneal models, such as geometry, material characterization and boundary conditions, and their application in the research field to extend the experimental results by including further relevant aspects and in the clinical field for diagnostic procedure, treatment and planning surgery. This review aims to analyse the state-of-art of the bioengineering techniques developed over the years to study the corneal biomechanics, highlighting their potentiality to improve diagnosis, treatment and healing process of the corneal tissue, and, at the same, pointing out the current limits in the experimental equipment and numerical tools that are not able to fully characterize in vivo corneal tissues non-invasively and discourage the use of finite element models in daily clinical practice for surgical planning.

Borel control and efficient numerical techniques to solve the Allen–Cahn equation governed by temporal multiplicative noise

In this manuscript, we investigate a stochastic version of the Allen–Cahn equation, which is a nonlinear partial differential equation from mathematical physics. The stochastic model considers temporal multiplicative noise in the form of the derivative of the standard Wiener process. The existence and the uniqueness of solutions for this stochastic model is established rigorously using the theory of distributions. As a corollary from these analytical results, some a priori optimal estimates for the solutions of this model are constructed. In this work, we develop reliable numerical schemes which possess similar features as those of the solutions for the analytical model. Moreover, we establish mathematically the von Neumann stability and the consistency for the schemes proposed in this paper. Both the analytical and numerical results derived in this work are computationally verified through some simulations.

Optimizing FPGA implementation of high-precision chaotic systems for improved performance.

Developing chaotic systems-on-a-chip is gaining much attention due to its great potential in securing communication, encrypting data, generating random numbers, and more. The digital implementation of chaotic systems strives to achieve high performance in terms of time, speed, complexity, and precision. In this paper, the focus is on developing high-speed Field Programmable Gate Array (FPGA) cores for chaotic systems, exemplified by the Lorenz system. The developed cores correspond to numerical integration techniques that can extend to the equations of the sixth order and at high precision. The investigation comprises a thorough analysis and evaluation of the developed cores according to the algorithm complexity and the achieved precision, hardware area, throughput, power consumption, and maximum operational frequency. Validations are done through simulations and careful comparisons with outstanding closely related work from the recent literature. The results affirm the successful creation of highly efficient sixth-order Lorenz discretizations, achieving a high throughput of 3.39 Gbps with a precision of 16 bits. Additionally, an outstanding throughput of 21.17 Gbps was achieved for the first-order implementation coupled with a high precision of 64 bits. These outcomes set our work as a benchmark for high-performance characteristics, surpassing similar investigations reported in the literature.

Heat transfer model analysis of fractional Jeffery-type hybrid nanofluid dripping through a poured microchannel

This study investigates the impact of coupled heat and mass transfer on the peristaltic migration of a magnetohydrodynamic (MHD) stress-strain Jeffery-type hybrid nanofluid flowing through an inclined asymmetric micro-channel with a porous medium. The fundamental two-dimensional momentum and energy transport equations are simplified under the assumptions of long wavelength and low Reynolds number. To solve the momentum and heat transfer problems, two advanced fractional derivative approaches are employed: the fractal integral and the Prabhakar fractional derivative. The pressure difference is determined using numerical integration techniques, such as the Stehfest and Tzou's algorithms. The results are presented through graphs and tables, which illustrate the effects of various parameters on the velocity, heat transfer, and trapping phenomena. As a result, we concluded that, pressure gradients grow with higher Reynolds numbers and channel-inclined angles. The heat transfer rate is observed to decrease as the Darcy number and the orientation of the electromagnetic field increase. When comparing the fractional derivative approaches, the fractal operator exhibits a more significant impact on the momentum profiles compared to the Prabhakar fractional operator. This difference is attributed to the distinct characteristics of the integral kernels associated with each fractional derivative definition. Furthermore, when comparing hybrid nanofluids, water-based (H2O + Ag + TiO2) hybrid fluids have a somewhat more significant effect than (C6H9NaO7 + Ag + TiO2) hybrid nanofluids.

Characterisation of the lightning strike damage mechanics onto composite materials and discussion on its numerical modelling techniques: review

Characterisation of the lightning strike damage mechanics onto composite materials and discussion on its numerical modelling techniques: review

Identification of the Aeromechanical Parameters of a Compressor Rotor from Blade Tip Timing Data

Abstract This article presents a maximum likelihood approach to identifying the mistuning, aerodynamic forcing functions, and aerodynamic influence coefficients of compressor rotor blades from noisy experimental measurements of blade deflection. The maximum likelihood estimation approach leads naturally to a nonlinear least squares optimization problem that can be solved using numerical optimization techniques such as quasi-Newton methods. An eigenmode decomposition approach is presented that permits the optimization objective function and gradient to be efficiently calculated so that the optimization is computationally feasible, even for experiments involving very large data sets. Simulation results show that the method has the potential to accurately identify the mistuning and aerodynamic nodal diameter forcing functions, but obtaining accurate results for influence coefficients may not be possible if there is significant disk flexibility. We demonstrate the method using both simulated and experimental blade vibration data from rotor 2 of the Purdue University three-stage axial compressor research facility collected using a light probe tip timing system as the rotor is slowly accelerated or decelerated through a Campbell diagram crossing.

A boundary point interpolation method for acoustic problems with particular emphasis on the calculation of Cauchy principal value integrals

A boundary point interpolation method (BPIM) is presented in this paper for numerical solving acoustic problems. The BPIM is a boundary-type meshless method that combines the point interpolation technique for constructing approximate functions with boundary integral equations for reformulating boundary value problems. Since effective numerical integration techniques are crucial in the BPIM and boundary integral equation methods for calculating regular and singular integrals, two Clenshaw-Curtis integration techniques (CCITs) for regular and weakly singular integrals are derived in a unified manner with the same integration points on quadratic integration cells. In addition, a unilateral CCIT, a power series expansion technique, and an improved CCIT are proposed to effectively calculate strongly singular integrals or Cauchy principal value integrals in the BPIM. These integration techniques provide direct and efficient formulas for calculating boundary integrals on quadratic integration cells, and can be directly applied to the calculation of regular and singular integrals in the boundary element method and other meshless boundary integral equation methods. Explicit expressions of integration weights in all CCITs are derived, and the values of integration points and weights are listed. Numerical results are finally provided to validate the effectiveness of the present meshless method and integration techniques.

Liquid induced vibrations of partially liquid-filled elastic cylindrical-conical shells

The main objective of this study to develop efficient numerical techniques based on coupled finite and boundary element methods to estimate natural vibration frequencies in compound reservoirs with liquid. Elastic structures composed of cylindrical and conical shells connected by rings have been examined. The space between the shells is filled with an ideal, incompressible fluid. The advantage of the proposed approach lies in the ability to investigate both free and forced vibrations of empty and liquid-filled shells structures within the framework of the single computer technology. The benchmark test calculations demonstrated the high accuracy and efficiency of the proposed approach. The novelty and practical value of the obtained results lie in the ability to investigate fuel tanks of complex shapes under various conditions.

Modification of extended Oxley’s predictive machining theory and determination of Johnson-Cook material model constants by inverse approach

The Johnson-Cook (J-C) flow stress model, renowned for its consideration of the combined effect of strain, strain-rate, and temperature on material property, forms the cornerstone of this research. Its simplicity and applicability in numerical simulation render it widely popular. The study addresses two primary objectives: first, to modify extended Oxley’s predictive machining theory by eliminating the iterative loop for calculating the tool-chip interface temperature, and second, to utilize an inverse approach for determining J-C material model constants specific to medium carbon steel. The modified approach successfully eliminates the iterative loop, thereby streamlining the determination process and effectively reducing calculation time by 25%–40%, thereby enhancing overall efficiency. Concurrently, the study employs an inverse approach to accurately determine the J-C constants (A, B, n, C, and m). Notably, the research avoids the need for expensive and time-consuming Split Hopkinson Pressure Bar (SHPB) tests, instead opting for low-cost axial tensile tests and numerical optimization techniques to obtain the J-C constants. Thus, this study provides a practical method for determining J-C constants, pivotal for accurate material representation in numerical simulations and metal cutting applications. Standard materials and machines are employed, ensuring ease of understanding for a wider audience. The predicted values for the J-C constants are in proximity to the experimental values obtained by using SHPB test. Validated findings, achieved with precision under specified metal cutting conditions, highlight the effectiveness and applicability of the proposed approach, providing valuable insights for optimizing machining processes and improving efficiency.

A closed-form Timoshenko beam element with multiple localized singularities for nonlinear material behavior using the strong discontinuity approach

The development of a novel closed-form beam element for nonlinear material behavior in structures is described, which is formulated according to Timoshenko beam theory and the embedded strong discontinuity approach. Multiple strong transverse and rotation discontinuities are considered to model several dissipative mechanisms due to localized singularities in the shear strain and curvature fields. Issues of dependence on numerical techniques, as occurs in displacement- and forced-based beam elements with the finite element method, are overcome since the formulated element is derived from a pure mathematical treatment. Theoretical principles are stemming from a Lagrangian variational model, from which singularities are naturally derived. The proposed formulation is solved by the conventional methods of calculus of variations, resulting in the boundary value problem. Then, closed-form expressions for any boundary conditions are obtained. By particularizing closed-form expressions for a basic system, a symmetric closed-form flexibility matrix is obtained. This matrix naturally leads to a symmetric closed-form stiffness matrix for any type of loading and unloading process, in which the nodeless degrees of freedom of the multiple embedded strong discontinuities are naturally condensed. Since Gauss integration methods are not used, the multiple localized singularities are not influenced by predefined positions of the integration points. However, the accuracy depends on the chosen number of singularities and their positions. Then, the proposed element is mesh independent when sufficient discontinuities are considered, which does not imply an increase in the degrees of freedom. Softening discontinuities are modeled at arbitrary positions in a single element, which overcomes the drawbacks of other embedded beam theories where more than one element is necessary to identify failure since strong discontinuities are generally located at the midpoint of the beam element. The obtained closed-form stiffness matrix is not always positive definite for strain-softening problems. Nevertheless, there are no major convergence issues as it is a symmetric matrix that does not require a constraint equation, so even the complex snap-back behavior in structures is adequately modeled. The capability of the formulated beam element for nonlinear material behavior in structures is validated with representative examples.

Quantifying Shape Transition in Anisotropic Plasmonic Nanoparticles through Geometric Inversion. Application to Gold Bipyramids.

Unraveling the nuanced interplay between the morphology and the optical properties of plasmonic nanoparticles is crucial for targeted applications. Managing the relationship becomes significantly complex when dealing with anisotropic nanoparticles that defy a simple description using parameters like length, width, or aspect ratio. This complexity requires computationally intensive numerical modeling and advanced imaging techniques. To address these challenges, we propose a detailed structural parameter determination of gold nanoparticles using their two-dimensional projections (e.g., micrographs). Employing gold bipyramids (AuBPs) as a model morphology, we can determine their three-dimensional geometry and extract optical features computationally for comparison with the experimental data. To validate our inversion model's effectiveness, we apply it to derive the structural parameters of AuBPs undergoing shape modification through oxidative etching. In summary, our findings allow for the precise characterization of structural parameters for plasmonic nanoparticles during shape transitions, potentially enhancing the comprehension of nanocrystal growth and optimizing plasmonic material design for various applications.

The new analytical and numerical analysis of 2D stretching plates in the presence of a magnetic field and dependent viscosity

This study explores heat transfer in a system involving Jeffery fluid of MHD flow and a porous stretching sheet. The mathematical representation of this system is initially described using a partial differential equation (PDE), which is then converted into an ordinary differential equation (ODE) through numerical techniques such as Lie similarity and transformation methods, along with the shooting approach. The results indicate that altering the variables of Jeffery fluid, heat source, porosity on a stretching sheet, and the physical characteristics of the magnetic field within the system leads to an upward trend. Implementing this enhanced heat transfer system can yield benefits across various domains, including industrial machinery, mass data storage units, electronic device cooling, etc., thereby enhancing heating and cooling processes. Furthermore, the study also utilized Akbari-Ganji’s Method, a new semi-analytical method designed to solve nonlinear differential equations of heat and mass transfer. The results obtained from this method were compared with those from the finite element method for accuracy, efficiency, and simplicity. This research provides valuable insights into heat transfer dynamics in complex systems and offers potential applications in various industrial settings. It also contributes to developing more efficient and effective heat transfer techniques.

Tafel Slope Plot as a Tool to Analyze Electrocatalytic Reactions.

Kinetic and nonkinetic contributions to the Tafel slope value can be separated using a Tafel slope plot, where a constant Tafel slope region indicates kinetic meaningfulness. Here, we compare the Tafel slope values obtained from linear sweep voltammetry to the values obtained from chronoamperometry and impedance spectroscopy, and we apply the Tafel slope plot to various electrocatalytic reactions. We show that similar Tafel slope values are observed from the different techniques under high-mass-transport conditions for the oxygen evolution reaction on NiFeOOH in 0.2 M KOH. However, for the alkaline hydrogen evolution reaction and the CO2 reduction reaction, no horizontal Tafel slope regions were observed. In contrast, we obtained the expected Tafel slope of 30 mV/dec for the HER on Pt in 1 M HClO4. We argue that widespread application of the Tafel slope plot, or similar numerical differentiation techniques, would result in an improved comparison of kinetic data for many electrocatalytic reactions when the traditional Tafel plot analysis is ambiguous.

Creasing and folding of paper-based sandwich material–Phenomena and modelling

Creasing and folding are fundamental steps in many manufacturing processes of multi-material paperboard packaging. The complex structure of these materials, which comprise layers of cellulose fibres, aluminium, and polyethylene, coupled with the growing complexity of packaging designs, make these process operations essential to ensure the required structural integrity for packaging as well as their functionality in daily life. This paper introduces an approach for modelling damage in paper-based sandwich materials by integrating fibre-based and cohesive numerical modelling techniques. The results prove the effectiveness of the proposed methodology, opening new possibilities for process design and optimization in packaging manufacturing.