Implementation Of Boundary Conditions Research Articles

Numerical simulation of 3D seismic wave based on alternative flux finite-difference WENO scheme

Summary High-frequency non-physical oscillations may occur due to shock waves in seismic wavefield and dynamic rupture simulation. In this study, we introduced the alternative flux finite-difference weighted essentially non-oscillatory (AWENO) scheme to address potential shock wave issues in computational seismology effectively. The wavefield of the body-fitted curvilinear domain was accurately computed through conservative grid mapping, ensuring accurate implementation of free surface boundary conditions on irregular surfaces using characteristic boundary conditions and minimizing artificial boundary reflections with exponential decay absorbing layers. Finally, we compared our scheme with the GRTM for flat surfaces and the CGFDM3D-EQR for irregular surfaces to demonstrate its correctness and accuracy, and validated its non-oscillatory characteristics. The aforementioned scheme is anticipated to assume a significant function in simulating more intricate seismic wavefields or dynamic ruptures.

Gulf Stream Effects on Sea Level Oscillations: Enhancing Performance of a Coastal and Estuarine Model Nested into Global Model through Modified Boundary Conditions

Gulf Stream Effects on Sea Level Oscillations: Enhancing Performance of a Coastal and Estuarine Model Nested into Global Model through Modified Boundary Conditions

THE ANALYSIS OF THE FLOW OF BLOOD IN A STENOSED ARTERY THROUGH SIMULATION: A COMPARISON AMONG VARIOUS NON-NEWTONIAN MODELS

This paper focuses on the dual quality of blood, Newtonian and non-Newtonian, in particular by exploring the energy curves. Careful investigation of the dual property of blood has been made by considering two different geometries to represent a stenosed arterial segment. We present a cautious assessment of non-Newtonian blood rheology impacts in arterial stream simulations by coupling the Newtonian and non-Newtonian models. The flow of energy through the two flow dimensions is meticulously investigated using velocity (kinetic energy), pressure, and wall shear stress (pressure energy). Besides, the proper implementation of an interface boundary condition (IBC) was emphasized to ensure consistency with the flow conditions downstream of a backward-facing step. The integration of the Newtonian and non-Newtonian models adjoins the novelty of the current research. The energy curves are obtained by implementing five different non-Newtonian models to designate a suitable non-Newtonian model for blood flow investigations. The combination of the non-Newtonian models enforced in this research is novel and particular attention is paid to the energy curves obtained. The conclusion was to elect the Carreau model as a suitable non-Newtonian rheological model for the blood flow study. This study was able to finalize the fact that the coupling of Newtonian and non-Newtonian models is necessary to obtain accurate results. For the sinusoidal waveform considered for the velocity, Carreau and the Power law models yield better results, eliminating the other non-Newtonian models from the list. With a better inlet condition imposed in the form of the Fourier series for pressure and velocity, the Carreau model yields the best results.

Implementation and validation of boundary conditions between a chemical reactor and ambient air

This work is dedicated to the development and validation of boundary conditions for a hot object cooled in a colder environment due to natural convection, radiation and evaporation. The main background of this research is to present boundary conditions for a hot reactor in cold ambient air, where the reactor walls are not thermally insulated. Water cooling in a standard small paper cup (coffee cup) was selected as a validation test. The experimental data comprise time histories of the cup’s side wall temperature measured using three thermoelements. The initial water temperature was set to 94 °C. The ambient air temperature was fixed at 25 °C and the air humidity at 20%. The computational model is based on unsteady laminar flow Navier–Stokes equations coupled with the heat transfer equation. The water density and all water transport properties (i.e., thermal conductivity, molecular viscosity, and specific heat capacity) are temperature-dependent. Numerical simulations in two-dimensional (2D) axisymmetry aligned well with the results from experiments. Including evaporative cooling on the top water surface proved essential to accurately determine the temperature profile. The boundary conditions are implemented into the Ansys Fluent 2022R2 computational fluid dynamics (CFD) commercial solver using user-defined functions (UDFs). The model equations can be used as a boundary condition for fixed beds and adsorption columns to improve the prediction of thermal profiles in both lab-scale and industrial-scale units.

An Enhanced Temperature Control Approach to Simulate Profile Extrusion.

Thermoplastic extrusion, a widely used method for processing thermoplastic materials, requires precise temperature control to ensure product quality. However, existing computer-aided engineering tools often oversimplify the temperature distribution calculations, leading to additional discrepancies between simulations and the actual processes. This study introduces a novel multi-region modeling approach to address this issue. By employing realistic temperature control conditions, the methodology overcomes the limitations of current numerical modeling tools. The key contributions include the development of a transient, incompressible, non-isothermal solver integrated into the OpenFOAM computational library and the implementation of a specialized boundary condition that emulates Proportional-Integral-Derivative (PID) control using real-time thermocouple measurements. The findings highlight temperature deviations at the flow channel walls and total pressure drop while demonstrating a smaller impact on velocity and flow uniformity at the outlet under steady-state conditions. This research substantially advances the understanding of thermal dynamics in extrusion processes, offering crucial insights for enhancing temperature control and laying the groundwork for more effective and precise operational strategies.

Rotation impact on the radial vibrations of frequency equation of waves in a magnetized poroelastic medium

This research delves into the propagation of radial free harmonic waves in a poroelastic cylinder, conceptualized as a magnetically and rotationaly influenced hollow structure. The primary aim is to elucidate the magnetic field's and rotation impact on the vibrational behavior of such systems. The investigative method encompasses the resolution of motion equations, formulated as partial differential equations, through the application of Lame's potential theory. This analytical process is augmented by the implementation of fitting boundary conditions, culminating in the derivation of a comprehensive expression for the complex dispersion equation, predicated on the premise that the wavenumber embodies a complex entity. The precision of the model is corroborated through a comparative analysis with established literature, underpinned by an exploration of diverse scenarios. The research employed MATLAB for both numerical and graphical assessments, focusing on the dispersion and displacement attributes. Dispersion relations within the poroelastic medium were computed, considering varied magnitudes of magnetic field intensity, rotation and angular velocities. The outcomes are articulated through complex-valued dispersion relations, transcendental formulations, and numerical resolutions employing MATLAB's bisection technique. These insights hold substantial significance for the theoretical advancement in orthopedic research, particularly concerning cylindrical poroelastic media. This study deduces that the radial vibrational patterns and the corresponding frequency equation within a poroelastic medium are profoundly modified by the magnetic field's interference and rotation. This study formulate a novel governing equation for a poroelastic medium, highlighting the significance of radial vibrations and investigating the impact of magnetic field and rotation.

Implementation of Non-Reflecting Boundary Conditions in the EFES Software Package for Solving Dynamic Contact Problems

Implementation of Non-Reflecting Boundary Conditions in the EFES Software Package for Solving Dynamic Contact Problems

Implementation of New Boundary Condition in LAMMPS for Energetics of Screw Dislocation in BCC Iron

Implementation of New Boundary Condition in LAMMPS for Energetics of Screw Dislocation in BCC Iron

Numerical study of the effect of a thin wire on the thermohydraulic performance in a plate fin-and-tube heat exchanger

A numerical study on the effect of a wire on the thermohydraulic performance in a plate-and-tube heat exchanger is performed with the Reynolds Averaged Navier-Stokes Equations approach. The heat exchanger is represented by a small finned tube bank with the implementation of periodic boundary conditions and symmetry conditions. The simulation models the turbulence with the Shear-Stress Transport model (SST k-ω). A benchmark case (without thin wire) is validated with PIV measurements of the horseshoe vortex and semi-empirical correlations for heat transfer. Then, twenty-four simulations are conducted at different dimensionless distances (1.0, 1.2, and 1.4) and angles (0, 15, 30, and 45°) of a thin wire. Predictions show that vortical structures around the thin wire contribute to an increase in thermohydraulic performance if the recirculation zones caused by thin wire do not affect the airflow patterns generated by finned tubes. However, the thermohydraulic performance decreases if airflow patterns are affected by the thin wire. Therefore, thin wire located at a dimensionless distance of 1.2 and angle of 15° generates a 5–6 % profit on the thermohydraulic performance with a pressure drop up to 73 Pa for Re = 2100.

Deep Learning-Based Prediction of Stress and Strain Maps in Arterial Walls for Improved Cardiovascular Risk Assessment

Conducting computational stress-strain analysis using finite element methods (FEM) is a common approach when dealing with the complex geometries of atherosclerosis, which is a leading cause of global mortality and complex cardiovascular disease. The considerable expense linked to FEM analysis encourages the substitution of FEM with a considerably faster data-driven machine learning (ML) approach. This study investigated the potential of end-to-end deep learning tools as a more effective substitute for FEM in predicting stress-strain fields within 2D cross sections of arterial walls. We first proposed a U-Net-based fully convolutional neural network (CNN) to predict the von Mises stress and strain distribution based on the spatial arrangement of calcification within arterial wall cross-sections. Further, we developed a conditional generative adversarial network (cGAN) to enhance, particularly from the perceptual perspective, the prediction accuracy of stress and strain field maps for arterial walls with various calcification quantities and spatial configurations. On top of U-Net and cGAN, we also proposed their ensemble approaches to improve the prediction accuracy of field maps further. Our dataset, consisting of input and output images, was generated by implementing boundary conditions and extracting stress-strain field maps. The trained U-Net models can accurately predict von Mises stress and strain fields, with structural similarity index scores (SSIM) of 0.854 and 0.830 and mean squared errors of 0.017 and 0.018 for stress and strain, respectively, on a reserved test set. Meanwhile, the cGAN models in a combination of ensemble and transfer learning techniques demonstrate high accuracy in predicting von Mises stress and strain fields, as evidenced by SSIM scores of 0.890 for stress and 0.803 for strain. Additionally, mean squared errors of 0.008 for stress and 0.017 for strain further support the model’s performance on a designated test set. Overall, this study developed a surrogate model for finite element analysis, which can accurately and efficiently predict stress-strain fields of arterial walls regardless of complex geometries and boundary conditions.

A general smoothed particle hydrodynamics (SPH) formulation for coupled liquid flow and solid deformation in porous media

The method of smoothed particle hydrodynamics (SPH) has been recently developed to study the coupled flow-deformation problems in porous material and considerable success has been achieved comparing to traditional mesh-based method, especially for treating large deformation and post-failure. However, computational challenges remain for the hydro-mechanical boundary treatment as well as the accuracy and stability of the numerical scheme. It is shown that the use of conventional SPH operator for the solution of the coupled problem can lead to several issues including numerical instabilities, inaccuracies and unphysical particle clumping as well as particle disorders near the boundary. To address these issues, a general SPH scheme with enhanced accuracy for saturated/unsaturated porous material is proposed in this paper. An improved SPH formulation for seepage analysis is proposed to allow an accurate prediction of liquid flow in porous material. A new stabilisation technique that combines the use of a density diffusion term, a modified particle shifting algorithm, and a new viscous damping term is developed to further improve the accuracy, stability and robustness of the proposed method. The implementations of stress boundary conditions and hydraulic boundary conditions in SPH, such as confining stress, hydraulic head, infiltration/evaporation, and potential seepage face, using either wall boundary particles or free-surface domain particles, are discussed in detail. A range of benchmark examples is adopted to verify the validity of the present coupled framework. The proposed model is finally applied to simulate the failure process of embankment dam due to rapid drawdown. Results indicate that the methodology proposed herein can be a promising tool for the analysis of the coupled hydro-mechanical process in porous material involving large deformations.

On the realization of periodic boundary conditions for hexagonal unit cells

In the context of homogenization of micro-heterogeneous materials, the choice of the Representative Volume Element (RV E) plays a crucial role. For periodic microstructures, an RV E is an underlying unit cell with periodic boundary conditions. Nevertheless, the question of the implementation of periodic boundary conditions may arise here; for example, some of the applications of periodic boundary conditions in the literature for hexagonal cells are incorrect or they are not given in detail. In this paper, we analyze periodic boundary conditions for two-dimensional hexagonal unit cells. Periodic boundary conditions are characterized by the periodic fluctuations in the displacement fields and anti-periodic traction vectors at associated points of the boundary of the unit cell. From comparative calculations with an ensemble of unit cells, it is evident that the natural choice for vanishing fluctuations is to be set on the midpoints of the six perimeter lines of the cell. The partially applied choice of vanishing fluctuations in the six corner points of the outer edge of the unit cell leads to wrong results. The boundary conditions proposed here are analyzed on the basis of representative examples and compared to the results with the incorrect boundary conditions.

Addressing Mass Conservation in Two-dimensional Modeling of Lithium Metal Batteries with Electrochemically Plated/Stripped Interfaces

Abstract This work investigates convection in liquid electrolytes induced by the movement of the lithium metal surface, modeled as a moving boundary. The back-and-forth motion of the lithium metal surface during the plating and stripping of lithium introduces a weak fluid motion in the liquid electrolyte that should be incorporated in the model equations and corresponding boundary conditions. The results for the electrochemical signatures and morphology evolution thus obtained by solving a coupled fluid model are compared with the case where the velocity distribution in the liquid electrolyte is ignored. This work extends our previously reported perspective on the convective flux correction at moving boundaries in one-dimensional models to two dimensions. This careful implementation of the correct boundary conditions ensures the mass conservation of lithium in two-dimensional simulations for predicting the morphological evolution of lithium metal electrodes over cycles. Additionally, these relative fluxes at the moving and fixed boundaries are sometimes ignored by assuming a bulk concentration condition at the far end, especially at the cathode/separator interface. While it may not affect overpotential signatures at the anode, it leads to mass conservation issues with implications for the accuracy of cycling simulations.

On Implementing Boundary Conditions for a Rate-Form Quasi-Static Contact Problem with Friction: A Node-to-Facet Finite Element Approach

On Implementing Boundary Conditions for a Rate-Form Quasi-Static Contact Problem with Friction: A Node-to-Facet Finite Element Approach

Investigation on smoothed finite element methods using linear tetrahedral elements for high-speed train hollow axle strength analysis

PurposeThis paper aims to investigate the performance of two novel numerical methods, the face-based smoothed finite element method (FS-FEM) and the edge-based smoothed finite element method (ES-FEM), which employ linear tetrahedral elements, for the purpose of strength assessment of a high-speed train hollow axle.Design/methodology/approachThe calculation of stress for the wheelset, comprising an axle and two wheels, is facilitated through the application of the European axle strength design standard. This standard assists in the implementation of loading and boundary conditions and is exemplified by the typical CRH2 high-speed train wheelset. To evaluate the performance of these two methods, a hollow cylinder cantilever beam is first used as a benchmark to compare the present methods with other existing methods. Then, the strength analysis of a real wheelset model with a hollow axle is performed using different numerical methods.FindingsThe results of deflection and stress show that FS-FEM and ES-FEM offer higher accuracy and better convergence than FEM using linear tetrahedral elements. ES-FEM exhibits a superior performance to that of FS-FEM using linear tetrahedral elements, showing accuracy and convergence close to FEM using hexahedral elements.Originality/valueThis study channels the novel methods (FS-FEM and ES-FEM) in the static stress analysis of a railway wheelset. Based on the careful testing of FS-FEM and ES-FEM, both methods hold promise as more efficient tools for the strength analysis of complex railway structures.

High-fidelity dynamics of piezoelectric covered metamaterial Timoshenko beams using the spectral element method

Piezoelectric metamaterial beams have received enormous research interest for the applications of vibration attenuation and/or energy harvesting in recent years. This paper presents a generic modelling approach for predicting the high-frequency dynamics of piezoelectric metamaterial beams. The spectral element method (SEM) is used to derive the dynamic stiffness matrix of a composite piezoelectric beam segment. Boundary condition implementations are demonstrated. Both band structure and transmittance analyses are realized. Several case studies for piezoelectric metamaterial beams configured in different geometric/electrical forms are carried out. The corresponding finite element (FE) models are built for verification, and a comparison study with the transfer matrix method (TMM) is conducted. For the uniform configurations, an almost indistinguishable difference is noted between the theoretical and FE results. For the stepped configurations, only minor discrepancies are observed in the high-frequency responses. The improved robustness and stability of the SEM method compared to the TMM method are demonstrated. A further discussion has been provided to explain the cause of the high-frequency discrepancies: sudden changes in the cross-section of the beam result in the stress concentration effect and reduce the bending stiffness at the junction connection. Finally, the value of the high-fidelity modelling approach is reflected through a parametric-based optimization study towards merging the Bragg scattering and locally resonant band gaps in an example piezoelectric metamaterial beam to achieve a wide band gap.

Modular Framework for the Solution of Boundary-coupled Multiphysics Problems

This paper presents a modular multiphysics framework developed for OpenFOAM. The framework is built around an iterative implicit coupling scheme based on a multi-region partitioned approach. This scheme allows the implementation of formal implicit time-marching schemes, which improves the stability of strongly interacting coupled problems. This methodology allows physical interactions to be handled through specifically designed interface boundary conditions. It also allows region-specific solvers to be implemented as modular class solvers. The coupling methodology is handled with a main program that manages solver-specific actions. The aim of this framework is to facilitate the implementation and testing of new multiphysics coupling problems in an integrated code structure. To show the capabilities of the framework to integrate new physics, solvers and boundary conditions requirements are discussed. Also, three validated examples involving fluid-structure interactions, conjugate heat transfer, and fluid-structure-thermal interactions are presented. Although all these problems are boundary-coupled multiphysics problems, the framework is conceptually not limited to this kind of problems. The benefit of this work to the OpenFOAM community is a general and modular framework that facilitates the setup and solution of diversified multiphysics problems, and that illustrates the implementation of modular interface boundary conditions between physics regions.

A flexible forcing immersed boundary scheme-based one-step simplified lattice Boltzmann method for two-dimensional fluid-solid interaction problems

In this study, we coupled the one-step simplified lattice Boltzmann method (OSLBM) [1] with flexible forcing immersed boundary (FFIB) scheme [2] and proposed a computationally efficient FFIB-OSLBM solver for complex two-dimensional fluid-solid interaction problems. The adopted OSLBM algorithm has the benefits of lower virtual memory requirement and easy implementation of physical boundary conditions over the traditional lattice Boltzmann (LBM) solver and is also computationally more efficient than the simplified lattice Boltzmann method (SLBM) [3]. Unlike in SLBM, the macroscopic variable is updated in one-step in OSLBM, thus avoiding the predictor and corrector steps and reducing the computational time. Furthermore, the adopted FFIB algorithm uses an implicit approach to calculate the body force density, which accurately satisfies the no-slip velocity condition at the boundary of the immersed solid. Moreover, this method requires less computational effort since it discards the time-consuming, complex matrix inversion process associated with the conventional immersed boundary (IB) method. We have conducted the numerical accuracy test and noticed that the proposed FFIB-OSLBM solver is nearly second-order accurate in space, which is higher than the typical coupled IB-LBM solvers. In addition, the applicability of the present solver is tested through a set of benchmark problems, and the results obtained from the present solver show an excellent agreement with the data available in the references. Compared to the FFIB-LBM [2], the present solver consumes at least 20% less computational memory and CPU time for all the validation problems investigated in this study.

A novel frequency-dependent lattice Boltzmann model with a single force term for electromagnetic wave propagation in dispersive media

Electromagnetic wave simulation is of pivotal importance in the design and implementation of photonic nano-structures. In this study, we developed a lattice Boltzmann model with a single extended force term (LBM-SEF) to simulate the propagation of electromagnetic waves in dispersive media. By reconstructing the solution of the macroscopic Maxwell equations using the lattice Boltzmann equation, the final form only involves an equilibrium term and a non-equilibrium force term. The two terms are evaluated using the macroscopic electromagnetic variables and the dispersive effect, respectively. The LBM-SEF scheme is capable of directly tracking the evolution of macroscopic electromagnetic variables, leading to lower virtual memory requirement and facilitating the implementation of physical boundary conditions. The mathematical consistency of the LBM-SEF with the Maxwell equations was validated by using the Champman-Enskog expansion; while three practical models were used to benchmark the numerical accuracy, stability, and flexibility of the proposed method.

LiDAR Point Cloud Data Combined Structural Analysis Based on Strong Form Meshless Method Using Essential Boundary Condition Capturing.

This study proposes a novel hybrid simulation technique for analyzing structural deformation and stress using light detection and ranging (LiDAR)-scanned point cloud data (PCD) and polynomial regression processing. The method estimates the edge and corner points of the deformed structure from the PCD. It transforms into a Dirichlet boundary condition for the numerical simulation using the particle difference method (PDM), which utilizes nodes only based on the strong formulation, and it is advantageous for handling essential boundaries and nodal rearrangement, including node generation and deletion between analysis steps. Unlike previous studies, which relied on digital images with attached targets, this research uses PCD acquired through LiDAR scanning during the loading process without any target. Essential boundary condition implementation naturally builds a boundary value problem for the PDM simulation. The developed hybrid simulation technique was validated through an elastic beam problem and a three-point bending test on a rubber beam. The results were compared with those of ANSYS analysis, showing that the technique accurately approximates the deformed edge shape leading to accurate stress calculations. The accuracy improved when using a linear strain model and increasing the number of PDM model nodes. Additionally, the error that occurred during PCD processing and edge point extraction was affected by the order of polynomial regression equation. The simulation technique offers advantages in cases where linking numerical analysis with digital images is challenging and when direct mechanical gauge measurement is difficult. In addition, it has potential applications in structural health monitoring and smart construction involving machine leading techniques.