Finite Element Method For Solving Research Articles

Investigation of friction modeling on numerical Ti6Al4V cutting simulations

Friction significantly influences chip formation, thereby highlighting its modeling critical in numerical cutting simulations. Notably, issues like the underestimation of feed force in simulations are often attributed to inadequate friction models. Nevertheless, diverse conclusions in the literature regarding friction’s behavior complicate the accurate implementation of this input. Additionally, the enormous number of the available friction models and their varied calibration methods introduce further debates over which aspects of friction modeling should receive more focus. These controversies and deficiencies hinder progress in further understanding friction’s role in chip formation through numerical studies. Instead of proposing or calibrating new friction models, the current study, based on Ti6Al4V machining simulations, attempts to readdress the aforementioned controversies in a neutral stance by conducting sensitivity studies using a hybrid Smoothed Particle Hydrodynamics (SPH) - Finite Element Method (FEM) solver with Graphics Processing Units (GPU) acceleration, which is capable of efficiently executing high-resolution computations. The significant impact of friction particularly at the end of the tool-chip contact on the chip formation, physical contact states and process forces are highlighted. The behaviors of physical parameters including normal contact pressure, sliding velocity, and temperature-dependent friction models in the literature are also evaluated. Several aspects such as the shear flow stress limit, the relationship between friction and process forces, and the selection of different models are discussed. In conclusion, pragmatic recommendations for friction modeling and cutting simulation work are provided. On the one hand, the available complex physical parameter dependent friction models could not prove their necessity and should be approached cautiously. Instead, the constant Coulomb friction model without the shear stress limit, despite its simplicity, demonstrates effective and sufficient for a single set of metal cutting simulations. On the other hand, reliable on-site measurement techniques of the coefficient of friction (COF) at the tool-chip sliding contact area should be developed, with consideration of the contact length and the state of material flow. Combined with careful cutting edge preparation and suitable constitutive models, the overall accuracy of numerical cutting simulations including the feed force prediction is expected to be improved.

Deep-Learning-Based Simulation and Inversion of Transient Electromagnetic Sounding Signals in Permafrost Monitoring Problem

Abstract —This article presents a novel approach to addressing the challenges in permafrost monitoring through the integration of deep-learning techniques with conventional electromagnetic sounding methods. Our methodology comprises a forward finite element method (FEM) solver, augmented with the Sumudu transform, and an artificial neural network (ANN) solver trained on FEM-generated data. Remarkably, the ANN solver demonstrates similar accuracy to the FEM solver but operates at a superior speed that is nearly 10,000 times faster. Furthermore, we introduce an inverse problem solution drawing on the PARS algorithm. In addition, we present an ANN-based inverse solver, where the input and output roles are inverted. The ANN inverse solver is trained on the same data, thereby offering an alternative approach to solving the inverse problem. In a computational experiment, we compare the numerical inversion results using the PARS algorithm with those obtained from the ANN forward solver, ANN inversion, and a linear combination of these solutions. This comprehensive analysis sheds light on the effectiveness of our deep-learning-based approach in permafrost monitoring, providing insights for future applications in geophysics and environmental science.

Wave energy conversion by an array of oscillating water columns deployed along a long-flexible floating breakwater

Large-scale spatial configurations combining Wave Energy Converters (WECs) and coastal attenuating-wave facilities have the potential to exploit marine renewable energy sustainably. In this study, an integrated concept of multiple Oscillating Water Columns (OWCs) and a very long floating breakwater is introduced. Associated energy extraction, gap resonance and hydroelastic interaction problems are examined. A coupled numerical simulation methodology consisting of a Finite Volume Method (FVM)based solver and a Finite Element Method (FEM) solver, is developed to investigate the strong fluid and structure coupled problem. The fluid-structure information is matched in real-time and the flexible modes of the floating breakwater are obtained by imposing a restrained beam inside the pontoon. The accurate time-domain model is validated against both simulated and measured data. Extensive parametric studies indicate that the energy conversion has a conflict with the wave attenuation in terms of determining the along-shore number of OWCs. The highest energy conversion in medium-period and long-period waves are observed in the OWCs near the end and middle locations, respectively. Besides, the constructive resonant gap effect between OWCs and the breakwater can amplify the peaks of energy conversion efficiency, leads to a sudden collapse in transmission coefficient curves. With an increased sidewall draft, OWCs closer to oblique incident direction generate stronger piston-type and sloshing oscillations. Additionally, compared with a rigid breakwater, the elastic deformation of the breakwater plays a destructive role in wave energy conversion, which is attributed to the out-of-phase interference of multi-mode radiated waves.

Semi-Analytical Approach versus Finite Element Method for Analysis of Propagation Properties in Rectangular Waveguides: Silica-Titania Technological Platform

This work explicitly demonstrates a semi-analytical effective index approximation (EIA) approach for the description of the propagation properties of rib and ridge waveguides. By using the example of waveguides realized on a low-cost silica-titania (SiO2:TiO2) technological platform, we present that EIA may be successfully applied for the approximate determination of modal effective indices and single mode propagation conditions. All obtained results have been confirmed to be convergent with the finite element method (FEM) simulations at low relative error. Due to the tremendously fast execution time of EIA simulations in comparison with the FEM solver, we believe that the presented approach may be applied in a preliminary step of designing functional blocks in new and existing photonic integrated circuit technologies, which often require complex and multi-parameter calculations.

Aerostructural Design Optimization of Wind Turbine Blades

This study presents an aerostructural optimization process for wind turbine blades aimed at enhancing the turbine’s performance. The optimization framework integrates DAFoam as the computational fluid dynamics (CFD) solver, TACS as the finite element method (FEM) solver, Mphys for fluid–structure coupling, and SNOPT as the optimizer within the OpenMDAO framework. The objective is to simultaneously increase the torque generated by the wind turbine while decreasing the mass of the blade, thereby improving its efficiency. The design variables in this optimization process are the blade shape and panel thickness. The aerodynamic objective function is torque, a key performance indicator for wind turbine efficiency. The structural objective function is the blade mass, as reducing mass is essential to minimize material and manufacturing costs. The optimization process utilizes the integrated capabilities of DAFoam, TACS, Mphys, and SNOPT to iteratively evaluate and modify the blade shape and panel thickness. The OpenMDAO framework facilitates seamless communication between the solvers and the optimizer, ensuring a well-coordinated, efficient optimization process. The results of the optimization show a 6.78% increase in torque, which indicates a significant improvement in the wind turbine’s energy production capacity. Additionally, a 4.22% decrease in blade mass demonstrates a successful reduction in material usage without compromising structural integrity. These findings highlight the potential of the proposed aerostructural optimization process to enhance the performance and cost-effectiveness of wind turbine blades, contributing to the advancement of sustainable energy solutions. This work represents the first attempt to implement DAFoam for wind turbine aerostructural design optimization.

An in silico testbed for fast and accurate MR labeling of orthopedic implants

One limitation on the ability to monitor health in older adults using magnetic resonance (MR) imaging is the presence of implants, where the prevalence of implantable devices (orthopedic, cardiac, neuromodulation) increases in the population, as does the pervasiveness of conditions requiring MRI studies for diagnosis (musculoskeletal diseases, infections, or cancer). The present study describes a novel multiphysics implant modeling testbed using the following approaches with two examples: (1) an in silico human model based on the widely available Visible Human Project (VHP) cryo-section dataset; (2) a finite element method (FEM) modeling software workbench from Ansys (Electronics Desktop/Mechanical) to model MR radio frequency (RF) coils and the temperature rise modeling in heterogeneous media. The in silico VHP-Female model (250 parts with an additional 40 components specifically characterizing embedded implants and resultant surrounding tissues) corresponds to a 60-year-old female with a body mass index of 36. The testbed includes the FEM-compatible in silico human model, an implant embedding procedure, a generic parameterizable MRI RF birdcage two-port coil model, a workflow for computing heat sources on the implant surface and in adjacent tissues, and a thermal FEM solver directly linked to the MR coil simulator to determine implant heating based on an MR imaging study protocol. The primary target is MR labeling of large orthopedic implants. The testbed has very recently been approved by the US Food and Drug Administration (FDA) as a medical device development tool for 1.5 T orthopedic implant examinations.

Massively parallel nodal discontinous Galerkin finite element method simulator for room acoustics

We present a massively parallel and scalable nodal discontinuous Galerkin finite element method (DGFEM) solver for the time-domain linearized acoustic wave equations. The solver is implemented using the libParanumal finite element framework with extensions to handle curvilinear geometries and frequency dependent boundary conditions of relevance in practical room acoustics. The implementation is benchmarked on heterogeneous multi-device many-core computing architectures, and high performance and scalability are demonstrated for a problem that is considered expensive to solve in practical applications. In a benchmark study, scaling tests show that multi-GPU support gives the ability to simulate large rooms, over a broad frequency range, with realistic boundary conditions, both in terms of computing time and memory requirements. Furthermore, numerical simulations on two non-trivial geometries are presented, a star-shaped room with a dome and an auditorium. Overall, this shows the viability of using a multi-device accelerated DGFEM solver to enable realistic large-scale wave-based room acoustics simulations.

An atomistic-continuum concurrent statistical coupling technique for amorphous materials using anchor points

A generalized framework for anchor point based concurrent coupling of finite element method (FEM) and molecular dynamics (MD) domains, incorporating previous related methods, is presented. The framework is robust and is agnostic of material crystallinity and atomistic description. The method follows an iterative approach to minimize the total energy of the coupled FEM-MD system, while maintaining displacement constraints between the domains. Two distinct forms of the coupling method are discussed in detail, differing in the nature of the constraint, both of which are able to make use of specialized MD solvers such as LAMMPS with little or no modification. Both methods make use of springs that join groups of atoms in the MD to the FEM domain. Method 1, termed ‘Direct Coupling’, couples MD anchor points directly to the FEM domain in a force-based manner and has the added advantage of being able to couple to specialized FEM solvers such as ABAQUS. Method 2 couples the MD to the FEM domain in a more ‘soft’ manner using the method of Lagrange multipliers and least squares approximation. The relative performance of these two methods are tested against each other in a uniaxial tension test using a graphene monolayer at 300 K temperature and a block of thermosetting polymer EPON862 at low temperature, showing comparable results. Convergence behaviour of the two coupling methods are studied and presented. The methods are then applied to the fracture of a centre-cracked graphene monolayer and compared with results from an identical pure MD simulation. The results corroborate the effectiveness of the developed method and potential use as a plug-and-play tool to couple pre-existing specialized FEM and MD solvers. Future work will focus on applying these methods to simulate elevated-temperature amorphous polymer models and their brittle fracture.

Efficient Newton‐multigrid FEM solver for multifield nonlinear coupled problems applied to thixoviscoplastic flows

AbstractThis note is concerned with efficient Newton‐multigrid finite element method (FEM) solver for multifield nonlinear flow problems. In our approach, for efficient FEM solver, we advantageously use the delicate symbiosis aspects of the problem settings for FEM approximations, and the algorithmic tools to obtain the numerical solutions. We concretize our ideas on thixoviscoplastic flow problems. It is a two‐field coupled nonlinear problem. And beside the integrated nonlinearity within momentum and microstructure equations, thixoviscoplastic problems induce a nonlinear two‐way coupling. As far as FEM numerical solutions are concerned, we set the problem in a suitable variational form to use the corresponding wellposedness analysis to develop FEM techniques for the solver. Indeed, the wellposedness study is not an intellectual exercise, rather it is the foundation for the approximate thixoviscoplastic problem as well as for the development of an efficient solver. We base our investigations for the solver on our wellposedness and error analysis results of thixoviscoplastic flow problems published in Proc. Appl. Math. Mech. We continue our series, and proceed to develop a monolithic Newton‐multigrid thixoviscoplastic solver. The solver is based on Newton's method and geometric multigrid techniques to treat the coupling of the problem. So, we use Local Pressure Schur Complement (LPSC) concept to solve the coupled problem on mesh's elements, and proceed with outer blocks Gauss‐Seidel iteration to update the global solutions. Furthermore, we handle the nonlinearity of the problem with the combined adaptive discrete Newton's and multigrid methods. The adaptivity within discrete Newton's method is based on the adaptive step‐length control for the discrete differencing in the Jacobian calculations, while the convergence of linear multigrid solver is made to match the convergence requirement of nonlinear solver, accordingly. And the solver's update parameters are solely dependent on the actual convergence rate of the nonlinear problem. We provide the numerical results of solver performance for thixoviscoplastic lid‐driven cavity flow.

Synergistic integration of deep neural networks and finite element method with applications of nonlinear large deformation biomechanics

Patient-specific finite element analysis (FEA) holds great promise in advancing the prognosis of cardiovascular diseases by providing detailed biomechanical insights such as high-fidelity stress and deformation on a patient-specific basis. Albeit feasible, FEA that incorporates three-dimensional, complex patient-specific geometry can be time-consuming and unsuitable for time-sensitive clinical applications. To mitigate this challenge, machine learning (ML) models, e.g., deep neural networks (DNNs), have been increasingly utilized as potential alternatives to finite element method (FEM) for biomechanical analysis. So far, efforts have been made in two main directions: (1) learning the input-to-output mapping of traditional FEM solvers and replacing FEM with data-driven ML surrogate models; (2) solving equilibrium equations using physics-informed loss functions of neural networks. While these two existing strategies have shown improved performance in terms of speed or scalability, ML models have not yet provided practical advantages over traditional FEM due to generalization issues. This has led us to the question: instead of abandoning or replacing the traditional FEM framework that can reliably solve biomechanical problems, can we integrate FEM and DNNs to enhance performance?In this study, we propose a synergistic integration of DNNs and FEM to overcome their individual limitations. Using biomechanical analysis of the human aorta as the test bed, we demonstrated two novel integrative strategies in forward and inverse problems. For the forward problem, we developed DNNs with state-of-the-art architectures to predict a nodal displacement field, and this initial DNN solution was then updated by a FEM-based refinement process, yielding a fast and accurate computing framework. For the inverse problem of heterogeneous material parameter identification, our method employs DNN as a regularizer of the spatial distribution of material parameters, aiding the optimizer in locating the optimal solution. In our demonstrative examples, despite that the DNN-only forward models yielded small displacement errors in most test cases; stress errors were considerably large, and for some test cases, the peak stress errors were greater than 50%. Our DNN-FEM integration eliminated these non-negligible errors in DNN-only models and was magnitudes faster than the FEM-only approach. Additionally, compared to FEM-only inverse method with errors greater than 50%, our DNN-FEM inverse approach significantly improved the parameter identification accuracy and reduced the errors to less than 1%.

A 2D elastic wall model to analyze the hyper‐viscous effects on blood flow across abdominal aortic aneurysm in COVID patients by fluid–structure interaction technique with ALE formulation

The worldwide dissemination of the coronavirus, as well as its dependencies, is being aided by detrimental urbanization. The impact of the viral infection upon an infected person is also thought to be influenced by any pre‐existing medical issues. Recent investigations have demonstrated that COVID‐19 patients have a higher degree of blood viscosity as a result of alterations in morphology in blood cells. Examining the importance of hyper‐viscosity in patients with COVID is crucial in determining the diseases of the arteries since viscosity is a key flow characteristic that affects the flow across a stenosis as well as an aneurysm. In the current study, a patient‐specific instance with an aneurysm across the abdominal aortal walls was taken into consideration. Given that abdominal aneurysms occur frequently in people, the high viscosity values are taken into account while examining the hyper‐viscous impact of fluid on its passage through the affected aorta. The current study is the initial endeavor to use the Arbitrary Lagrangian–Eulerian (ALE) Technique to study the impact of fluid–structure interaction (FSI) on the movement of fluid across an aneurysmal aortal section in conjunction with hyper‐viscous anomalous blood characteristics. The investigation backs up the different medical results that described the negative consequences of blood hyper‐viscosity. The computational findings from employing a finite element method (FEM) solver to resolve the fluid mechanical computations complemented alongside the solid mechanical principles indicate a possibility that the increased stress imposed by the hyper‐viscous propagates on the interior walls of the aneurysmal aorta may prompt the aneurysmal pouch to grow or breakdown. Also, the hyper‐viscous blood in COVID patients destroys the smooth muscle cells of the media layer endangering its normal structure and functions and leading to the development of new aneurysms.

6G Broadband and High Directive Microstrip Antenna with SIW and FSSs

Sixth-Generation (6G) wireless communication networks require the fabrication of broadband and high directivity microstrip antennas to offset the high atmospheric path loss beyond 100 Gigahertz (GHz). In this paper, we designed and proposed a couple of high-gain and broadband microstrip array antennas that have been designed within a Finite Integration Technique (FIT) solver at Computer Simulation Technology Microwave Studio (CST MWS) software in a series-parallel feeding method for a resonance frequency above 107 GHz. A Substrate-Integrated Waveguide (SIW) with dual outputs has been used at these antennas and with WR-08 waveguide that covers the 90-140 GHz frequency range, while the first was without Frequency Selective Surfaces (FSSs), and the second was with the FSSs to increase the antenna directivity further. The first design was simulated with a Finite Element Method (FEM) solver at Ansys High-Frequency Structure Simulator (HFSS) to compare the simulation results of this antenna. This comparison's peak gain and Bandwidth (BW) were correspondingly 25.3 dB, 12.5 GHz, 23.1 dB, and 11 GHz from the Ansys HFSS and the CST MWS. Thus, the accuracy and the slight deviation of the compared simulation results from each other validated the offered 6G antenna designs. Therefore, after experimental verification, the proposed antennas can be employed in 6G future wireless communication networks.

Contacting Micro Asperity of a Deformable Surface

Abstract Deterministic contact modeling based on half-space theories has satisfied a wide range of applications. However, the half-space theories themselves do not involve shape effects of roughness on Green’s functions/influence coefficients; in deterministic rough-surface contact analyses, the roughness is considered in gap function. This approach can be called the “roughness simplification.” One needs to answer two questions about the validity of the roughness simplification: How appropriate is the roughness simplification in modeling rough-surface contacts? How accurately can the commonly included contact-plasticity behavior be captured under the roughness simplification? This work utilized a double-scale representation of an asperity—a microscopic deformable asperity stacked on a deformable half-space, to obtain their combined contact responses in both elastic and plastic regimes. The deformation and contact behaviors of asperities thus configured were obtained with finite element analysis (FEA) and rough-surface half-space contact solvers. Three stages of asperity contact were discovered: the Hertzian stage, the single-region elastoplastic stage, and the two-region elastoplastic stage where the surrounding base material also takes part in the contact. The comparisons of contact deformation and pressure results from both the finite element analysis and half-space contact solvers support the validity of the half-space theories with the roughness simplification for various ellipsoid-shape asperities with circular-bases in both elastic and elastoplastic rough-surface asperity modeling. The research also reveals that when significant plastic deformations occur, asperities with different aspect ratios can bear different maximum elastoplastic contact pressures.

A coupled FEM-DEM study on mechanical behaviors of granular soils considering particle breakage

Particle breakage often occurs in the fields of geological, geotechnical and hydraulic engineering like rock avalanche, landslides and high earth-rock dam, which affects the design and countermeasures of relevant engineering structures. Investigation of particle breakage’s effect on mechanical behaviors of granular soils has always been the hotspot within the community of particulate materials. In this study, a coupled finite element method (FEM) and discrete element method (DEM) modeling has been developed to tackle boundary value problems (BVPs) related with particle breakage. In the method, the particle breakage simulation is implemented in DEM through the conventional bonded particle modeling (BPM), while the stress–strain characteristics of representative volume element (RVE) captured by DEM is directly transmitted into the FEM solver to avoid the complicated and phenomenological constitutive equations incorporating into particle breakage. As an illustration, we apply the proposed multiscale modeling to investigating mechanical behaviors of quartz sands subjected to particle breakage through the high confining pressure biaxial compression simulation. And effects of particle strength, particle shape and confining pressure on particle breakage characteristics and further mechanical behaviors of quartz sands are also discussed accompanied with the underlying micromechanisms. Results demonstrate that the coupled FEM-DEM modeling can be able to deal with the complex geomechanics problems involving particle breakage.

Computational Optimization of Irradiance and Fluence for Interstitial Photodynamic Therapy Treatment of Patients with Malignant Central Airway Obstruction.

There are no effective treatments for patients with extrinsic malignant central airway obstruction (MCAO). In a recent clinical study, we demonstrated that interstitial photodynamic therapy (I-PDT) is a safe and potentially effective treatment for patients with extrinsic MCAO. In previous preclinical studies, we reported that a minimum light irradiance and fluence should be maintained within a significant volume of the target tumor to obtain an effective PDT response. In this paper, we present a computational approach to personalized treatment planning of light delivery in I-PDT that simultaneously optimizes the delivered irradiance and fluence using finite element method (FEM) solvers of either Comsol Multiphysics® or Dosie™ for light propagation. The FEM simulations were validated with light dosimetry measurements in a solid phantom with tissue-like optical properties. The agreement between the treatment plans generated by two FEMs was tested using typical imaging data from four patients with extrinsic MCAO treated with I-PDT. The concordance correlation coefficient (CCC) and its 95% confidence interval (95% CI) were used to test the agreement between the simulation results and measurements, and between the two FEMs treatment plans. Dosie with CCC = 0.994 (95% CI, 0.953-0.996) and Comsol with CCC = 0.999 (95% CI, 0.985-0.999) showed excellent agreement with light measurements in the phantom. The CCC analysis showed very good agreement between Comsol and Dosie treatment plans for irradiance (95% CI, CCC: 0.996-0.999) and fluence (95% CI, CCC: 0.916-0.987) in using patients' data. In previous preclinical work, we demonstrated that effective I-PDT is associated with a computed light dose of ≥45 J/cm2 when the irradiance is ≥8.6 mW/cm2 (i.e., the effective rate-based light dose). In this paper, we show how to use Comsol and Dosie packages to optimize rate-based light dose, and we present Dosie's newly developed domination sub-maps method to improve the planning of the delivery of the effective rate-based light dose. We conclude that image-based treatment planning using Comsol or Dosie FEM-solvers is a valid approach to guide the light dosimetry in I-PDT of patients with MCAO.

Energy Dissipation on an Elastic Interface as a Metric for Evaluating Three Friction Models

Abstract The effect of three different friction interface models on an elastic half-space is presented. Three constitutive friction models are studied: Coulomb, soil–concrete interface, and Bouc–Wen, using a computational mechanics framework that can represent the contact patch's material response to static and dynamic surface tractions. This response is observed as strains and stresses present from reciprocating sliding using an elastoplastic friction (EPF) algorithm that also captures energy dissipation and hysteresis due to friction sliding. Additionally, the use of the four-parameter Bouc–Wen model represents a new development in contact mechanics that allows micro-slip of the contact interface to be modeled. Hysteresis loops are generated for the three friction models based on a quasi-static assumption. This algorithm is built into a mesoscale finite element method solver that is able to simulate different loading conditions and provide insight into how the friction models respond to load conditions and inform on experimental data. The energy dissipation from reciprocating friction sliding will be generated for each friction model as a metric that captures surface wear and potential material damage.

A fast adaptive PD-FEM coupling model for predicting cohesive crack growth

In this study, nonlocal theory of peridynamic (PD) is coupled with finite element method (FEM) to simulate cohesive crack growth in quasi-brittle materials. The adaptive dynamic relaxation method is adopted to implement quasi-static loading conditions. The advantage of peridynamic method in the modeling of crack propagation is taken into consideration to be coupled with that of finite elements which is computationally less expensive and covers various boundary value problems. In this novel method, the whole domain of the problem is initially dominated by FEM solver with coarse mesh grids. Coupling process is then introduced to those regions which have critical conditions according to damage criterion. The capability of the proposed coupling method in the modeling of cohesive crack growth in quasi-brittle materials is demonstrated. In comparison to other conventional PD-FEM coupling methods, the computational cost of the proposed method is considerably improved and total running time of the solution is significantly attenuated. The validity of the method is confirmed through comparing the results with experimental ones.

Hybrid SPH-FEM solver for metal cutting simulations on the GPU including thermal contact modeling

This paper presents a hybrid Smoothed Particle Hydrodynamics (SPH) – Finite Element Method (FEM) solver for metal cutting simulations on Graphics Processing Units (GPU). For the first time in chip formation simulation, the heat transfer between an SPH model of the workpiece, and a transient FEM temperature model for the cutting tool, is established. For validation, the performance of the modeled thermal contact between two numerical domains is compared with a commercial FEM software. The sensitivity of the implemented SPH-FEM contact parameters is investigated for the first time and further insights into the thermal modeling of cutting simulations are generated. Overall, the newly developed hybrid model saves the computational time on the cutting tool side in the pure SPH method and enables more efficient high-fidelity cutting simulations. By clearly defining the thermal contact at the tool-chip interface, the simulated tool surface temperature agrees well with the experimental measurements in the literature.

Efficient prediction of airborne noise propagation in a non-turbulent urban environment using Gaussian beam tracing method

This paper presents a noise propagation approach based on the Gaussian beam tracing (GBT) method that accounts for multiple reflections over three-dimensional terrain topology and atmospheric refraction due to horizontal and vertical variability in wind velocity. A semi-empirical formulation is derived to reduce truncation error in the beam summation for receivers on the terrain surfaces. The reliability of the present GBT approach is assessed with an acoustic solver based on the finite element method (FEM) solutions of the convected wave equation. The predicted wavefields with the two methods are compared for different source-receiver geometries, urban settings, and wind conditions. When the beam summation is performed without the empirical formulation, the maximum difference is more than 40 dB; it drops below 8 dB with the empirical formulation. In the presence of wind, the direct and reflected waves can have different ray paths than those in a quiescent atmosphere, which results in less apparent diffraction patterns. A 17-fold reduction in computation time is achieved compared to the FEM solver. The results suggest that the present GBT acoustic propagation model can be applied to high-frequency noise propagation in urban environments with acceptable accuracy and better computational efficiency than full-wave solutions.

Possibilities for the Flow of Water and Blood through a Graphene Layer in a Geometry Analogous to Human Arterioles: An Observational Study

Atherosclerosis and aneurysm are two non-communicable diseases that affect the human arterial network. The arterioles undergo dimensional changes that prominently influence the flow of oxygen and nutrients to distal organs and organ systems. Several studies have emerged discussing the various possibilities for the circumstances surrounding the existence of these pathologies. In the present work, we analyze the flow of blood across the stenosis and the aneurysmic sac in contrast with the flow of water to explore alterations in the flow characteristics caused by introduction of the graphene layer. We investigate the blood flow past the graphene layer with varying porosity. The study is undertaken to replace usage of a stent along a blocked artery by inserting a thin layer of graphene along the flow channel in the post-pathological section of the geometry. To explain the flow, a 2D mathematical model is constructed, and the validity and exclusivity of the model’s solution are examined. When the artery wall is assumed to be inelastic, the computation of the mathematical system is evaluated using a finite element method (FEM) solver. We define a new parameter called critical porosity Cεp to explore the flow possibilities through the graphene layer. The findings indicate that the flow pattern was adversely affected by the graphene layer that was added to the flow field. The negative impact on the flow could be due to the position of the graphene layer placed. The Cεp values for the flow of blood across healthy arteriole, stenosed arteriole, and aneurysmic arteriole segments were 5.7%, 3.5%, and 3.5% respectively. The critical porosity values were achieved with precision in terms of linear errors 8.1×10−12, 7.7×10−12, and 3.9×10−12, respectively. The consequences of the present study disclose various possible ways to utilize graphene and its compounds in the medical and clinical arena, with a prior exploration of the chemical properties of the compound. The idea and the methodology applied for the present study are novel as there have been no previous research works available in this direction of the research field.