Boundary Conditions Research Articles

Lid driven flow and heat transfer due to various positions of slit in a square cavity: FEM approach

A detailed analysis of flow and heat transfer due to moving slit within the various positions of the square cavity is discussed. The slit is strategically positioned and examined at three distinct locations within the square cavity i.e. left, middle and right. Constraints of the square cavity are defined for horizontal and vertical walls. The top horizontal wall is considered to be adiabatic while the other three walls of the cavity are cold. The upper surface of slit is heated and movable towards the left side of the square cavity while the other three walls are immovable and cold. The fluid flow dynamics and heat transfer within the enclosed cavity are governed by fundamental principles of mass, momentum and energy conservation. These governing principles manifest as intricate mathematical equations, specifically nonlinear partial differential equations accompanied with boundary conditions. The key parameters under consideration include the Reynolds number (250≤Re≤1500) and Richardson number (0.01≤Ri≤5) at a fixed Prandtl number (Pr=6.2). These parameters are analysed through variations in velocities, temperature profiles, isotherms and streamlines. In the computational framework, the momentum and temperature equations are addressed through quadratic interpolation, while linear interpolation is applied to handle the pressure equation. The numerical solution, utilizing Newton's technique and the PARADISO solver, is rigorously validated against existing research methodologies, establishing its methodological reliability. Higher Reynolds numbers shift the primary vortex towards the middle and create corner recirculation zones, more uniform heat distribution, while higher Richardson numbers increase buoyancy forces, reducing isotherm contours and affecting heat distribution. The local Nusselt number increases with the increase in Reynolds numbers but shows small changes with the increase in Richardson number. The value of Nusselt number decreases as the position of slit changes from left to right.

Kernel-Based Minimal Distributed Charges: A Conformationally Dependent ESP-Model for Molecular Simulations.

A kernel-based method (kernelized minimal distributed charge model (kMDCM)) to represent the molecular electrostatic potential (ESP) in terms of off-center point charges is introduced. The positions of the charges adapt to the molecular geometry and allow the description of intramolecular charge flow. Using Gaussian kernels and atom-atom distances as the features, the ESPs for water and methanol are shown to improve by at least a factor of 2 compared with point charge models fit to an ensemble of structures. The conformationally fluctuating molecular dipole moment of water is reproduced almost twice as accurately using kMDCM compared with static PCs, despite not fitting to the dipole directly. The role of hyperparameters in the kernelization is investigated and their implication on model performance and simulation stability is discussed. Combining kMDCM for the electrostatics and reproducing kernels for the bonded terms allows energy-conserving simulations of 2000 water molecules with periodic boundary conditions on the nanosecond time scale. These MD simulations sample geometries outside the training set but remain stable, which demonstrates the robustness of the model and its implementation.

The Effect of Unsteady Inlet Boundary Conditions on the Aero-Thermal Behavior of High-Pressure Turbine Vanes – A Numerical Study Using Scale-Resolving Simulations

Abstract This paper presents the application of a novel method to prescribe unsteady boundary conditions to transient, scale-resolving computational fluid dynamics simulations of the high-pressure turbine in modern jet engines. The methodology is based on the compression of the interface data at the combustor–turbine interface, using proper orthogonal decomposition and Fourier series (PODFS). Doing so can reduce the stored data at the interface drastically. The capability of the PODFS method to produce realistic inlet boundary conditions was demonstrated in previous work. Here, the method is applied to a turbine case. The outlet data of a combustor simulation is used to create the PODFS boundary conditions for a scale-resolving simulation of a simplified first nozzle guide vane of the high-pressure turbine. This simulation is compared with simulations with steady-state boundary conditions to show the effect of unsteadiness in the inlet boundary condition on the aerodynamic and thermal behaviors of the turbine. While the aerodynamics show minor sensitivity against the way of applying the inlet boundary conditions, the thermal behavior of the vanes is strongly affected by the modeling of combustor unsteadiness.

Extended B‐spline‐based implicit material point method for saturated porous media

AbstractThe large deformation and fluidization process of a solid–fluid mixture includes significant changes to the temporal scale of the phenomena and the shape and properties of the mixed material. This paper presents an extended B‐spline (EBS)‐based implicit material point method (EBS‐MPM) for the coupled hydromechanical analysis of saturated porous media to enhance the overall versatility of MPM in addressing such diverse phenomena. The proposed method accurately represents phenomena such as high‐speed motion in both the quasi‐static and dynamic states by employing a full formulation of coupled hydromechanical modeling. The weak imposition of boundary conditions based on Nitsche's method allows representing the boundary conditions independent of the relative position of the particles and computational grid. In addition, it enables dynamic changes in the boundary domain based on the deformation. The robustness of this boundary representation is reinforced using EBS basis functions, which prevent the degradation of the condition number of the system matrices regardless of the position of the boundary domain with respect to the computational grid. Furthermore, a stabilization method based on a variational multiscale method (VMS) approach is employed to provide the flexibility in choosing arbitrary basis functions for spatial discretization, facilitating the effective construction of EBS. Numerical examples including comparisons between a full formulation and a simplified formulation are presented to demonstrate the performance of the developed method under various boundary conditions and loading states across different time scales.

Study on Wind Farm Flow Field Characteristics Based on Boundary Condition Optimization of Complex Mountain Numerical Simulation

The accurate prediction of the flow field characteristics of complex mountains is of great practical significance for the development and construction of wind farms, but it is not yet fully understood. The main purpose of this study is to propose a method for the study of flow field characteristics under complex mountain conditions, which can optimize the boundary conditions required for numerical simulation through the wind acceleration ratio and, at the same time, couple the numerical simulation and wind measurement data to reflect the real mountain flow field distribution. The results show that the proposed method has good applicability in complex mountain wind farms, can reproduce the real flow field distribution, and has a certain practical value. Wind speed distribution and turbulence intensity are greatly affected by boundary conditions such as wind speed and wind direction and are also affected by the shielding effect brought by terrain changes. The contrast between 120° and 150° wind direction is more obvious. When the incoming wind moves to the top of a mountain or the ridgeline, it will form a low-speed wake area behind it, resulting in reduced wind speed, increased turbulence intensity, and an unstable flow field.

The overdetermined Cauchy problem for the hyperbolic Gellerstedt equation

Abstract Overdetermined boundary value problems and the minimal operators generated by them are extremely important in the description of regular boundary value problems for differential equations, and are also widely used in the study of local properties of solutions. In addition, for inverse problems of mathematical physics arising from applications, when determining unknown data, it is necessary to study problems with overdetermined boundary conditions, which is reflected in the study of problems, including for hyperbolic equations and systems, arising in physics, geophysics, seismic tomography, geoelectrics, electrodynamics, medicine, ecology, economics and many other practical areas. Thus, the study of overdetermined boundary value problems is of both theoretical and applied interest. In this paper, a criterion for the regular solvability of the overdetermined Cauchy problem for the Gellerstedt equation and the minimal differential operator generated by it in a hyperbolic domain is established, as which both the case of a characteristic triangle and the case of a more general domain with fairly general assumptions about the boundary of the domain are considered. Due to overdetermined boundary conditions, the problem under consideration will be ill-posed in the general case, therefore, for its regular solvability, additional conditions must be imposed on the initial data. In other words, we have considered the inverse problem: to determine what requirements the initial data of the problem, in particular the right part of the Gellerstedt equation, should meet, in question, so that the overdetermined Cauchy problem is regularly solvable. The proof is based on the Gellerstedt potential, the properties of solutions of the Goursat problem in the characteristic triangle, and the properties of special functions.

Analytical and Numerical Investigation of Star Polymers in Confined Geometries

The analysis of the impact of the star polymer topology on depletion interaction potentials, depletion forces, and monomer density profiles is carried out analytically using field theory methods and techniques as well as molecular dynamic simulations. The dimensionless depletion interaction potentials and the dimensionless depletion forces for a dilute solution of ideal star polymers with three and five legs (arms) in a Θ-solvent confined in a slit between two parallel walls with repulsive surfaces and for the case where one of the surfaces is repulsive and the other inert are obtained. Furthermore, the dimensionless layer monomer density profiles for ideal star polymers with an odd number (f˜ = 3, 5) of arms immersed in a dilute solution of big colloidal particles with different adsorbing or repelling properties in respect of polymers are calculated, bearing in mind the Derjaguin approximation. Molecular dynamic simulations of a dilute solution of star-shaped polymers in a good solvent with N = 901 (3 × 300 + 1 -star polymer with three arms) and 1501 (5 × 300 + 1 -star polymer with five arms) beads accordingly confined in a slit with different boundary conditions are performed, and the results of the monomer density profiles for the above-mentioned cases are obtained. The numerical calculation of the radius of gyration for star polymers with f˜ = 3, 5 arms and the ratio of the perpendicular to parallel components of the radius of gyration with respect to the wall orientation for the above-mentioned cases is performed. The obtained analytical and numerical results for star polymers with an odd number (f˜ = 3, 5) of arms are compared with our previous results for linear polymers in confined geometries. The acquired results show that a dilute solution of star polymer chains can be applied in the production of new functional materials, because the behavior of these solutions is strictly correlated with the topology of polymers and also with the nature and geometry of confined surfaces. The above-mentioned properties can find extensive practical application in materials engineering, as well as in biotechnology and medicine for drug and gene transmission.

Determining pressure from velocity via physics-informed neural network

This paper describes a physics-informed neural network (PINN) for determining pressure from velocity where the Navier-Stokes (NS) equations are incorporated as a physical constraint, but the boundary condition is not explicitly imposed. The exact solution of the NS equations for the oblique Hiemenz flow is utilized to evaluate the accuracy of the PINN and the effects of the relevant factors including the boundary condition, data noise, number of collocation points, Reynolds number and impingement angle. In addition, the PINN is evaluated in the two-dimensional flow over a NACA0012 airfoil based on computational fluid dynamics (CFD) simulation. Further, the PINN is applied to the velocity data of a flying hawkmoth (Manduca) obtained in high-speed schlieren visualizations, revealing some interesting pressure features associated with the vortex structures generated by the flapping wings. Overall, the PINN offers an alternative solution for the problem of pressure from velocity with the reasonable accuracy and robustness.

Resolvent Analysis for Subsonic Compressor With Impedance Boundary Condition Casing Treatment

Abstract A resolvent analysis framework for the axial compressor is established, and the impedance optimization is achieved based on the resolvent analysis framework for the impedance boundary condition casing treatment. This framework is derived by treating the nonlinearity in the perturbation equations as an unknown forcing, the linear relationship between wall impedance and energy gains is obtained. The validity of this framework is confirmed through experiments on rotating inlet distortion, which captures the most susceptible frequency for the stall points of the compressor. The resolvent analysis framework further confirms that the first-order circumferential mode exhibits the highest energy in the given cases. Subsequently, the proposed impedance optimization method is tested under throttling operating conditions, especially focusing on the first-order circumferential mode. The introduction of a favorable impedance boundary condition notably reduces energy gain within the low-order circumferential mode and in the range of the rotor rotating frequency, particularly in near-stall operating conditions. The energy suppression mechanism of the impedance boundary condition casing treatment is investigated, demonstrating that the impedance boundary condition, with an optimal impedance value, significantly suppresses perturbations compared to the case with the solid wall boundary condition. Lastly, a design method for the impedance boundary condition casing treatment is discussed, offering a reliable theoretical design tool for enhancing the stall margin of axial compressors.

Coupled model for liquid lithium plasma facing components

Numerical analysis provides the design choice and operating window of liquid metal Plasma Facing Components (PFC) concepts. Coupled analysis of boundary plasma together with the surrounding boundary structures is required. To achieve this goal, PPPL is developing a comprehensive multi-physics model for modeling of PFCs in fusion devices. The model includes the fluid-kinetic code SOLPS-ITER and the flow and heat transfer code CFX from ANSYS. SOLPS-ITER was augmented with a liquid metal boundary condition algorithm, allowing direct two-way coupling of the plasma analysis with the two-dimensional analytical slab flow model which includes heat convection in the liquid metal PFC. The target heat flux resulting from this coupled analysis is used as a boundary condition for detailed 3D Computational Fluid Dynamics (CFD) Magneto Hydro Dynamics (MHD) and heat transfer analysis. A new formulation of MHD equations is introduced in the numerical procedure ensuring current conservation of the discretized equations. Results of the 3D analysis are used for final validation of the coupled model. A PFC design where a porous wall is used to stabilize the liquid metal surface, while MHD drive is used to push the liquid metal flow inside the PFC, will be investigated in the regimes where vapor shielding is created for enhanced volumetric plasma heat dissipation.

Analysis of a Bifurcation and Stability of Equilibrium Points for Jeffrey Fluid Flow through a Non-Uniform Channel

This study aims to analyze how the parameter flow rate and amplitude of walling waves affect the peristaltic flow of Jeffrey’s fluid through an irregular channel. The movement of the fluid is described by a set of non-linear partial differential equations that consider the influential parameters. These equations are transformed into non-dimensional forms with appropriate boundary conditions. The study also utilizes dynamic systems theory to analyze the effects of the parameters on the streamline and to investigate the position of critical points and their local and global bifurcation of flow. The research presents numerical and analytical methods to illustrate the impact of flow rate and amplitude changes on fluid transport. It identifies three types of streamline patterns that occur: backwards, trapping, and augmented flow resulting from changes in the value of flow rate parameters.

Electromagnetic wave scattering in plasma beam-driven waveguides under strong magnetic fields

This study analyzes the scattering of electromagnetic waves in a cold and uniform plasma-filled waveguide driven by an intense relativistic plasma beam under a strong magnetic field. The strong interaction of plasma with electromagnetic waves enables its potential use in different types of waveguides. The Helmholtz equation governs the boundary value problem, which is solved by incorporating the mode matching technique. Invoking the boundary and matching conditions and the derived orthogonality and dispersion relations in this scheme gives an exact solution to the scattering problem. The numerical results shed light on the occurrence of reflection and transmission and flow of power. The power flux is plotted against angular frequency and various duct configurations. The solution is completely validated through the benefit of analytical and numerical results. The investigation of this structure reveals not only its mathematical, but also its physical features.

On a class of third-order dissipative differential operator with distributional potentials

This paper aims to investigate a class of boundary value problems generated by a third-order differential equation with distributional potentials and some dissipative boundary conditions. We first construct an operator related to the problem, then prove that the operator is dissipative and show some eigenvalue properties of this operator. Further using Krein’s theorem we prove the completeness theorems of the operator.

Effects of topological boundary conditions on Bell nonlocality

Effects of topological boundary conditions on Bell nonlocality

Does extremes lead to opposites? The influence mechanism of specific ambivalent emotions on tourists’ travel intention

ABSTRACT Emotions are an important basis for decision making, and their influence is increasingly attracting attention from the academic community. However, existing research mainly focuses on the impact of a single emotion on people and lacks information on the impact of ambivalent emotions. Based on the Cognitive-Affective processing system theory, this study explores tourists’ willingness to travel, while experiencing the emotions of hope and anxiety through two situational experiments. This study used the Sojump platform to recover data, and a total of 200 valid samples were collected in Experiment 1 to explore the chain-mediating role of proactive coping and well-being. A total of 240 valid samples were collected in Experiment 2, which verified the boundary conditions of the interaction between hope and anxiety on tourists’ willingness to travel. The results broaden the theoretical research on tourism ambivalence and provide a reference source for tourism companies to use ambivalence in precision marketing.

Free vibration analysis of an O-pattern graphene reinforced axial functionally graded polymer matrix nano-composite non-uniform beam

Recently, the demand for nanocomposites in the form of functionally graded materials (FGM) has increased because of their improved weight-to-stiffness ratios, less delamination effects, and ability to have desired qualities at the right location. Additionally, compared to typical composites, static qualities like strength and elasticity are superior. In this research work, a model for an axially graphene-reinforced functionally graded polymer matrix nanocomposite non-uniform beam is prepared, to obtain the dynamic behavior of the beam in form of its Natural Frequencies. Along the length of the beam, the graphene Nano reinforcement is dispersed in an epoxy polymer matrix as “O” pattern using a function. Material modulus at each location of the beam is modelled using Halpin-Tsai micromechanics theory, the mass density and Poisson’s Ratio of the beam are determined using rule of mixture. The geometry non-uniformity of the beam is modelled using an exponential function. Using MATLAB software code, simulation and parametric analysis of the beam are performed for various slenderness ratios and varied boundary conditions. The non-uniform beam result is obtained after the result for a uniform beam is used to validate it. In result it is analyzed that for the particular geometric and reinforcement configuration of the beam, as the non-uniformity in the beam geometry is increases, the fundamental frequency decreases, and the slenderness ratio has also the same effect on its fundamental frequency.

Anisotropic obstacle Neumann problems in weighted Sobolev spaces and variable exponent

Abstract In this paper we focus on a certain class of anisotropic obstacle problems governed by a Leray–Lions operator. This problem is subject to homogeneous Neumann boundary conditions. By applying truncation techniques and the monotonicity method, we establish the existence of entropy solutions for the problem studied in the framework of anisotropic weighted Sobolev spaces with variable exponent.

Micromagnetic behavior of permalloy (Ni80Fe20) nanodots as a function of aspect ratio

We present the results of computational micromagnetic simulations at zero temperature under free boundary conditions for Permalloy nanodots. The nanodot’s diameter (D) was varied from 20 to 120 nm, and the thickness (t) ranged from 4 to 120 nm, which allows to obtain different aspect ratios t/D. Simulations were conducted using the Ubermag platform and the Object Oriented Micromagnetic Framework (OOMMF). The hysteresis loops exhibited a strong dependence on the aspect ratio (t/D), which was evident in the narrowing of the hysteresis curves as this ratio approached unity. This phenomenon led to the formation of nucleation and annihilation fields, resulting in the formation of vortex-type magnetic textures with a central core capable of moving within the basal plane. Furthermore, the time dynamics at each step of the magnetic field were addressed by solving the time-dependent Landau-Lifshitz-Gilbert differential equation, where the system’s Hamiltonian is defined in terms of magnetocrystalline anisotropy, demagnetization, exchange, and Zeeman contributions. Energy diagrams illustrate the competition among these energies, attempting to attain their equilibrium state, thereby creating a complex energy landscape. Moreover, they operate on different orders of magnitude, whence their relative importance is discussed. Final results are summarized in a proposal of phase diagrams.

The limit case in a nonlocal $p$-Laplacian equation with dynamical boundary conditions

The limit case in a nonlocal $p$-Laplacian equation with dynamical boundary conditions

Analysis of acoustic radiation problems involving arbitrary immersed media interfaces by the extended finite element method with Dirichlet to Neumann boundary condition

To quantify the influence of moving immersed media on acoustic radiation, this study develops an efficient method for acoustic radiation with arbitrary immersed media interfaces based on the extended finite element method (XFEM) and the Dirichlet-to-Neumann (DtN) boundary condition. The XFEM is employed for efficient and accurate modeling of the acoustic field with boundary shape variations. It requires no modification of the computational mesh and accurately captures non-smooth solutions on the interface by constructing enrichment functions. Additionally, the DtN boundary condition simulates the far-field radiation condition by establishing the relationship between the acoustic pressure and its derivatives. Numerical examples show that the proposed method efficiently characterizes changes in the position of immersed media interfaces without re-meshing the mesh. Variations in the thickness of porous material domains alter the acoustic radiation characteristics, with thicker porous material domains resulting in more pronounced noise reduction effects. Compared to changes in the thickness of porous material domains, changes in their position significantly alter the distribution of radiation pressure, indicating that ideal noise reduction effects can be achieved by strategically placing porous materials in specific locations in practical engineering applications.