Fictitious Boundary Research Articles

Enhanced fully resolved CFD-DEM-PBFM simulation of non-spherical particle–fluid interactions during hydraulic collection

The interactions between non-spherical particles and fluids are commonplace in both nature and engineering applications, such as deep-sea nodules hydraulic collection. However, accurately simulating granular particles with non-spherical shapes and gaining a deep understanding of the intricate mechanisms involved in fluid–particle interactions still pose significant challenges. In this study, the superquadric model and the Gaussian curvature model are introduced in the Discrete Element Method to describe particle shapes and characterize their nonlinear contact behavior, respectively. Simultaneously, the Fictitious Domain-Immersed Boundary Method (FD-IBM) and the Particle Boundary Field Method (PBFM) are employed to enhance the stability and accuracy of numerical simulations. Building upon these advancements, an extended resolved CFD-DEM-PBFM method is developed. The validation and superiority of this resolved CFD-DEM-PBFM method are rigorously verified by comparing its results with the experimental and other research results across various scenarios, including non-spherical particle collision and packing, particle settling, drafting-kissing-tumbling test, and flow around non-spherical particles. Subsequently, the application of our novel model has been further conducted by a case study that simulates the hydraulic collection of nodules with different aspect ratios l/d. Concurrently, the influences of the nodule shapes on the hydraulic collection mechanism of the hydraulic collection are unveiled in terms of suction forces, trajectory of the particle, and flow field characteristics. Our findings demonstrate that the extended resolved CFD-DEM-PBFM method excels at accurately characterizing multiphase interaction mechanisms at both macro and micro scales, presenting considerable advantages in simulating fluid-particle systems involving non-spherical particles.

Method of Fundamental Solutions without Fictitious Boundary in Elastodynamic Behavior Using Dual Reciprocity Method

Method of Fundamental Solutions without Fictitious Boundary in Elastodynamic Behavior Using Dual Reciprocity Method

Exploring causality in braneworld/cutoff holography via holographic scattering

Holography with branes and/or cutoff surfaces presents a promising approach to studying quantum gravity beyond asymptotically anti-de Sitter spacetimes. However, this generalized holography is known to face several inconsistencies, including potential violations of causality and fundamental entropic inequalities. In this work, we address these challenges by investigating the bulk scattering process and its holographic realization. Specifically, we propose that the information on a brane/cutoff surface Q propagates according to the induced light cones originating from a fictitious asymptotic boundary behind Q, rather than the conventional ones originating from a point on Q. Additionally, we establish the validity of the connected wedge theorem for generalized holography with induced light cones. We also demonstrate that entropic inequalities remain valid within the induced causal diamonds. While the induced light cone seemingly permits superluminal signaling, we argue that this causality violation can be an artifact of state preparation for radially propagating excitations, rather than local operator excitations on Q.

Computational Study of Twin Circular Particles Settling in Fluid using a Fictitious Boundary Approach

Computational Study of Twin Circular Particles Settling in Fluid using a Fictitious Boundary Approach

A Novel ANN-Based Radial Basis Function Collocation Method for Solving Elliptic Boundary Value Problems

Elliptic boundary value problems (BVPs) are widely used in various scientific and engineering disciplines that involve finding solutions to elliptic partial differential equations subject to certain boundary conditions. This article introduces a novel approach for solving elliptic BVPs using an artificial neural network (ANN)-based radial basis function (RBF) collocation method. In this study, the backpropagation neural network is employed, enabling learning from training data and enhancing accuracy. The training data consist of given boundary data from exact solutions and the radial distances between exterior fictitious sources and boundary points, which are used to construct RBFs, such as multiquadric and inverse multiquadric RBFs. The distinctive feature of this approach is that it avoids the discretization of the governing equation of elliptic BVPs. Consequently, the proposed ANN-based RBF collocation method offers simplicity in solving elliptic BVPs with only given boundary data and RBFs. To validate the model, it is applied to solve two- and three-dimensional elliptic BVPs. The results of the study highlight the effectiveness and efficiency of the proposed method, demonstrating its capability to deliver accurate solutions with minimal data input for solving elliptic BVPs while relying solely on given boundary data and RBFs.

Current-induced scouring around a submarine pipeline using a multi-phase flow model with different inter-phase drag models

This paper numerically investigates scouring beneath a submarine pipeline induced by the current. The simulations use an Eulerian–Eulerian multi-phase model for sediment transport developed in OpenFOAM (the open-source Computational Fluid Dynamic toolbox), which can capture fluid–particle–structure interactions. The model implements the Hybrid Fictitious Domain-Immersed Boundary (HFD-IB) method for representing the pipeline structure in the computational domain. The simulated flow fields are validated by experimental data for the developed flow around a pipeline over scoured beds, resulting in favorable results for velocity profiles. Further, three inter-phase drag models, the EF (Engelund and Fredsøe, 1976), RZ (Richardson and Zaki, 1997), and ERZ (Lee and Huang, 2018) are applied and subsequently examined in simulating pipeline scouring, particularly the effects on the flow field, sediment transport, and the resulting scour profile during the onset and tunnel erosion stages. The models produce consistent results with the measured scour profile. All models show that buoyancy is dominant in driving the sand movements within and near the bed surface in both stages. Meanwhile, the drag force is dominant for sand transport above the bed where the inter-phase relative velocity is high. However, the three models differently capture the physical behaviors of the particle response time and relative velocity near the bed surface and within the bed, which impact the computed drag force and, thus, the resulting scour profile.

Non-Convex Particle-in-Cell Model for the Mathematical Study of the Microscopic Blood Flow

The field of fluid mechanics was further explored through the use of a particle-in-cell model for the mathematical study of the Stokes axisymmetric flow through a swarm of erythrocytes in a small vessel. The erythrocytes were modeled as inverted prolate spheroids encompassed by a fluid fictitious envelope. The fourth order partial differential equation governing the flow was completed with Happel-type boundary conditions which dictate no fluid slip on the inverted spheroid and a shear stress free non-permeable fictitious boundary. Through innovative means, such as the Kelvin inversion method and the R-semiseparation technique, a stream function was obtained as series expansion of Gegenbauer functions of the first and the second kinds of even order. Based on this, analytical expressions of meaningful hydrodynamic quantities, such as the velocity and the pressure field, were calculated and depicted in informative graphs. Using the first term of the stream function, the drag force exerted on the erythrocyte and the drag coefficient were calculated relative to the solid volume fraction of the cell. The results of the present research can be used for the further investigation of particle–fluid interactions.

Mathematical Modeling of Coolant Flow in Discontinuous Drilling Processes with Temperature Coupling

AbstractNickel‐based alloys, like Inconel 718, are widely used in industrial applications due to their high‐temperature strength and high toughness. However, machining such alloys is a challenging task because of high thermal loads at the cutting edge and thus extensive tool wear is expected. Consequently, the development of new process strategies is needed. We will consider the discontinuous drilling process with coolant. The main idea is to interrupt the drilling process in order to let the coolant to flow around the cutting edge and to reduce thermal loads. Since measurements inside the borehole are (nearly) impossible, simulations are a key tool to analyze and understand the proposed process.In this paper, a 3D fluid flow simulation model with Q2P1 Finite Elements in combination with the Fictitious Boundary Method is presented to simulate the coolant flow around the drill inside the borehole. The underlying equations are transformed into a rotational frame of reference overcoming the challenges of mesh design for high rotational domains inside the fluid domain. Special treatment of Coriolis forces is developed, that modifies the ‘Pressure Poisson’ Problem in the projection step improving the solver for high angular velocities. To further take high velocities into account, a two‐scale artificial diffusion technique is introduced to stabilize the simulation. Finally, Q1 Finite Elements are used to simulate the heating and cooling processes in both the tool and the coolant during the complete discontinuous drilling process. The simulation is split into a ‘contact’ and a ‘no contact’ phase and a coupling strategy between these phases is developed. FBM is utilized to switch between the two configurations, thus only one unified grid for both configurations is needed. The results are used to gain insight into the discontinuous drilling process and to optimize the process design.

A SFBEM–FEM coupling method for solving crack problems based on Erdogan fundamental solutions

The boundary element method (BEM) has proven to be an efficient approach for crack analysis in fracture mechanics, while its versatility in application to crack problems of complex structures with irregular boundaries deserves further attention. In this study, to improve the applicability to complex crack analysis, a cracked superelement is first established with BEM to model the near-crack region, and the crack problem is then solved within the frame of finite element method (FEM). The stiffness matrix of the cracked superelement is formulated using the spline fictitious boundary element method (SFBEM) based on the Erdogan fundamental solutions for an infinite plane with a single crack. The proposed superelement is further incorporated into a finite element mesh to simulate the behaviour of the crack zone, and the governing equation of the crack problem is finally established and solved using the typical procedure of FEM. After obtaining the nodal displacements of the superelement, the stress intensity factors (SIFs) of crack tips can be obtained by a backward analysis with SFBEM. The accuracy and efficiency of the proposed SFBEM–FEM coupling method are demonstrated by two numerical examples involving a rectangular plate with a central crack and a square plate with 100 horizontal cracks. The present approach is further applied to the analysis of the SIFs of multiple cracks exposed in a steel anchorage box for a hanger of a suspension bridge, which indicates the merging of the cracked superelements to the commercial FEM software is computationally efficient for the analysis of complex structures with multiple cracks.

Transient Dynamic Response Analysis of Two-Dimensional Saturated Soil with Singular Boundary Method

In this paper, the singular boundary method (SBM) in conjunction with the exponential window method (EWM) is firstly extended to simulate the transient dynamic response of two-dimensional saturated soil. The frequency-domain (Fourier space) governing equations of Biot theory is solved by the SBM with a linear combination of the fundamental solutions. In order to avoid the perplexing fictitious boundary in the method of fundamental solution (MFS), the SBM places the source point on the physical boundary and eliminates the source singularity of the fundamental solution via the origin intensity factors (OIFs). The EWM is carried out for the inverse Fourier transform, which transforms the frequency-domain solutions into the time-domain solutions. The accuracy and feasibility of the SBM-EWM are verified by three numerical examples. The numerical comparison between the MFS and SBM indicates that the SBM takes a quarter of the time taken by the MFS.

Indirect boundary element formulation with dual reciprocity in elastodynamics

In this paper, a new indirect boundary element formulation for two-dimensional elastodynamic problems is presented. The formulation makes use of a static fundamental solution. For accurate solution, the location of the fictitious boundary is chosen to be the same as problem boundary. The relevant fundamental solution is integrated over lines. The method is combined with the Dual Reciprocity Method (DRM), for handling the domain integral concerning to the domain inertia terms. A suitable approximation (traditional function C-R is used) for the inertia terms (or, domain accelerations), is used to transform the domain integral to the boundary. The discretization is performed on the boundary, or a boundary-like geometry. The method is easy to code and efficient as presented by the numerical examples.

Numerical simulation of early stages of scour around a submarine pipeline using a two-phase flow model

Current-induced scour around a submarine pipeline during onset and tunnel erosion are investigated in both clear-water and live-bed regimes using an Eulerian–Eulerian two-phase model for sediment transport. The Hybrid Fictitious Domain-Immersed Boundary (HFD-IB) method is adopted to simulate the pipeline structure. The model is validated against two published experimental data: (1) flow past a pipeline near a rigid bed and (2) scour around a pipeline over a sand-bed, showing favorable results for the flow and scour patterns around the pipe. The driving mechanisms of the onset and tunnel erosion are investigated by examining the detailed fluid–sediment interactions around the pipe in both regimes. The driving mechanisms for the onset and tunnel erosion are found similar in both regimes, except their time and magnitude scales. The onset is triggered by the piping mechanism induced by the upstream–downstream pressure gradient beneath the pipe. Meanwhile, the jet flow is the driving mechanism for the tunnel erosion. The simulated live-bed condition shows a higher upstream–downstream pressure gradient beneath the pipe, faster piping mechanism, more intense jet flow velocity and sediment flux compared to the clear-water condition. The model well capture these underlying mechanisms, suggesting its promising capability as a predictive tool for scouring.

Active Electric Dipole Energy Sources: Transduction via Electric Scalar and Vector Potentials.

The creation of electromagnetic energy may be realised by engineering a device with a method of transduction, which allows an external energy source, such as mechanical, chemical, nuclear, etc., to be impressed into the electromagnetic system through a mechanism that enables the separation of opposite polarity charges. For example, a voltage generator, such as a triboelectric nanogenerator, enables the separation of charges through the transduction of mechanical energy, creating an active physical dipole in the static case, or an active Hertzian dipole in the time-dependent case. The net result is the creation of a static or time-dependent permanent polarisation, respectively, without an applied electric field and with a non-zero vector curl. This system is the dual of a magnetic solenoid or permanent magnet excited by a circulating electrical current or fictitious bound current, respectively, which supplies a magnetomotive force described by a magnetic vector potential and a magnetic geometric phase proportional to the enclosed magnetic flux. Thus, the active electric dipole voltage generator has been described macroscopically by a circulating fictitious magnetic current boundary source and exhibits an electric vector potential with an electric geometric phase proportional to the enclosed electric flux density. This macroscopic description of an active dipole is a semi-classical average description of some underlying microscopic physics, which exhibits emergent nonconservative behaviour not found in classical closed-system laws of electrodynamics. We show that the electromotive force produced by an active dipole in general has both electric scalar and vector potential components to account for the magnitude of the electromotive force it produces. Independent of the electromagnetic gauge, we show that Faraday’s and Ampere’s law may be derived from the time rate of change of the magnetic and dual electric geometric phases. Finally, we analyse an active cylindrical dipole in terms of scalar and vector potential and confirm that the electromotive force produced, and hence potential difference across the terminals is a combination of vector and scalar potential difference depending on the aspect ratio (AR) of the dipole. For long thin active dipoles (AR approaches 0), the electric field is suppressed inside, and the voltage is determined mainly by the electric vector potential. For large flat active dipoles (AR approaches infinity), the electric flux density is suppressed inside, and the voltage is mainly determined by the scalar potential.

Hybrid fictitious domain-immersed boundary solver coupled with discrete element method for simulations of flows laden with arbitrarily-shaped particles

Particle-laden flows are commonly encountered in numerous engineering applications, e.g. fluidization, crystallization, granulation, drying, catalytic cracking, food processing, biomass gasification, or suspension and slurry transport in general. However, computational fluid dynamics (CFD) simulations containing freely moving and irregularly shaped bodies are still a challenging topic. More so, if the bodies are densely distributed and large enough to affect the fluid flow. In the present work, we propose a finite volume based CFD solver for mathematical modeling of the flow-induced movement of interacting irregular particles. The modeling approach uses a hybrid fictitious domain-immersed boundary method for inclusion of the solids. The bodies movements and contacts are solved via discrete element method (DEM). The new solver is implemented within the OpenFOAM framework, validated against data from literature, and utilized in simulations of catalytic washcoat deposition in a filter for automotive exhaust gas aftertreatment, considering a realistic size distribution of non-spherical catalyst microparticles.

Elasticity problems of beams on reaction-driven nonlocal foundation

A challenging task in nonlocal continuum mechanics consists in formulating constitutive relations leading to well-posed structural problems. Several strategies have been adopted to overcome issues inherent applicability of Eringen’s pure nonlocal theory to nanostructures, such as local/nonlocal mixtures of elasticity and integral models involving modified averaging kernels. These strategies can be applied to the ill-posed problem of flexure of a beam on Wieghardt nonlocal foundation without considering any fictitious boundary forces of constitutive type. A consistent formulation of nonlocal elastic foundation underlying a Bernoulli–Euler beam is thus conceived in the present paper by requiring that transverse displacements are convex combination of reaction-driven local and nonlocal phases governed by Winkler and Wieghardt laws, respectively. The proposed integral mixture is proven to be equivalent to a more convenient differential problem, equipped with nonlocal boundary conditions, which can be effectively exploited to solve nonlocal problems of beams resting on mixture reaction-driven continuous foundation. Effectiveness of the developed nonlocal approach is illustrated by analytically solving simple elasto-static problems of structural mechanics.

Numerical Analysis Of a Falling Circular Particle Passing through a Fluid Channel having Diamond Shaped Obstacles

It has been analyzed that the particle motion inside a vertical channel while passing across diamond shaped obstacles produces severe effects on the fluid. Particle interaction with outer boundary, internal obstacles and with the fluid is inspected. An Eulerian based approach using a computational mesh is used in which solid particles are allowed to move freely in fluid domain. Fluid and particle interaction inside the whole domain is carried using Fictitious boundary method (FBM). A multigrid finite element method combined with the fictitious boundary method (FEM-FBM) is used for the simulation of in-compressible fluid flow along with rigid particle falling and colliding inside a fluid domain. A collision model to treat the Particle-obstacle and particle-wall interactions is used to avoid particle overlapping. The particulate flow is evaluated using an open source multigrid finite element solver FEATFLOW. Numerical investigations are executed in view of different particle positions and different alignment of diamond shaped obstacles. Effects on the movement of the particle and on the interaction of the fluid-particle system due to particle-wall, particle-Obstacle, particle-fluid interactivity has been analyzed.

A novel localized collocation solver based on a radial Trefftz basis for thermal conduction analysis in FGMs with exponential variations

This paper introduces a novel localized radial Trefftz collocation method (LRTCM) for steady-state heat conduction analysis in 2D and 3D functionally graded materials (FGMs) with exponential variations. The LRTCM is constructed by combining the traditional radial Trefftz collocation method (RTCM) and the localized collocation scheme. In the proposed LRTCM, the radial Trefftz basis of the heat conduction equation in FGMs is derived by the variable transformation and domain mapping method, and the approximation solution at each node is expressed as a linear combination of a radial Trefftz basis in each local subdomain, thus the resulting sparse linear system naturally satisfies governing equation at interior nodes and boundary conditions at boundary nodes. The LRTCM not only inherits the advantages of the RTCM (meshlessness, no fictitious boundary and high accuracy), but also works well in large-scale structures or with more complicated boundary conditions when compared to the RTCM. Finally, the feasibility, accuracy, efficiency and stability of the proposed method are investigated by three examples.

On the Schwarz method for the eddy currents model

We investigate an iterative solver for the reduced eddy currents model set in open domains. Its formulation is the result of the coupling of a variational problem restricted to a truncated domain with a transparent condition at the fictitious boundary. The non-local boundary condition is derived using simple/double layer potentials. Applying a splitting technique yields an iterative algorithm that requires to solve, at each iteration, a local Neumann boundary value problem on the current potential. A re-interpretation of the algorithm as a Schwarz method enables a tractable convergence analysis which is the core subject of the paper. Using suitable variational tools, we establish an exponential convergence of the iterative solver. Some analytical and numerical examples are presented to check the theoretical findings and the relevance of our procedure.

Wall effects on a falling solid particle in an infinite channel

We have examined the effects caused on the motion and sedimentation of a free falling solid particle by the hydrodynamic forces acting on the particle’s surface arising when particle is close to wall. Drag and lift coefficients for a settling particle inside a narrow domain are calculated. An Eulerian mesh is adopted for computing the motion of free moving solid particles through the domain. The combined particle and fluid mixture is treated with a fictitious boundary method approach. To avoid particle-wall collisions, an approach proposed by Singh, Glowinsk and coauthors is used to handle such interactions. The particulate flow is computed using multigrid finite element solver FEATFLOW (Finite element analysis tool for flow problems). Numerical experiments are performed by decreasing domain widths for a single falling particle. The size and density of the particle is varied to inspect the particle paths. The behavior of the particle and its interaction with wall while it is moving inside constricted domains is analyzed. Results for the drag and lift forces on the surface of particle are presented and compared with the reference values.

On the Analytical Solution of the Kuwabara-Type Particle-in-Cell Model for the Non-Axisymmetric Spheroidal Stokes Flow via the Papkovich–Neuber Representation

Modern engineering technology often involves the physical application of heat and mass transfer. These processes are associated with the creeping motion of a relatively homogeneous swarm of small particles, where the spheroidal geometry represents the shape of the embedded particles within such aggregates. Here, the steady Stokes flow of an incompressible, viscous fluid through an assemblage of particles, at low Reynolds numbers, is studied by employing a particle-in-cell model. The mathematical formulation adopts the Kuwabara-type assumption, according to which each spheroidal particle is stationary and it is surrounded by a confocal spheroid that creates a fluid envelope, in which the Newtonian fluid moves with a constant velocity of arbitrary orientation. The boundary value problem in the fluid envelope is solved by imposing non-slip conditions on the surface of the spheroid, which is also considered as non-penetrable, while zero vorticity is assumed on the fictitious spheroidal boundary along with a uniform approaching velocity. The three-dimensional flow fields are calculated analytically for the first time, in the spheroidal geometry, by virtue of the Papkovich–Neuber representation. Through this, the velocity and the total pressure fields are provided in terms of a vector and the scalar spheroidal harmonic potentials, which enables the thorough study of the relevant physical characteristics of the flow fields. The newly obtained analytical expressions generalize to any direction with the existing results holding for the asymmetrical case, which were obtained with the aid of a stream function. These can be employed for the calculation of quantities of physical or engineering interest. Numerical implementation reveals the flow behavior within the fluid envelope for different geometrical cell characteristics and for the arbitrarily-assumed velocity field, thus reflecting the different flow/porous media situations. Sample calculations show the excellent agreement of the obtained results with those available for special geometrical cases. All of these findings demonstrate the usefulness of the proposed method and the powerfulness of the obtained analytical expansions.