Interior Boundary Research Articles

Isogeometric indirect boundary element method for solving the 3D acoustic problems

This paper provides an Isogeometric Indirect Boundary Element Method (IGIBEM) based on NURBS (Non-Uniform Rational B-Splines) and PHT-splines (polynomial splines over hierarchical T-meshes) for analyzing the three-dimensional (3D) acoustic problems. In the classical procedure, the geometries are discretized by Lagrange polynomials elements, which leads to both substantial geometrical error and time-consuming meshing steps. However, these deficiencies can be eliminated by the isogeometric analysis (IGA) directly incorporating the geometry description generated from the CAD (Computer Aided Design) software into CAE (Computer Aided Engineering) analysis. Unlike the DBEM (direct boundary element method), the IBEM (indirect boundary element method) allows different types of boundary conditions on the two sides of a surface. Moreover, the hypersingular integrals in IBEM can be transformed to a weakly singular form. In addition, the PHT-based IBEM is used to investigate the influence of local refinement on the accuracy of solutions. Finally, the non-uniqueness problem is solved, which is a fatal defect in the acoustic BEM for the exterior problem. Four different methods to handle the non-uniqueness problem are discussed and compared. The results obtained by the proposed method were compared with analytical solutions and the results computed by Lagrange-based IBEM. Several benchmark examples demonstrate: (1) the present method, i.e. IGIBEM, has super accuracy over conventional IBEM for the acoustic problems; (2) local refinement has a significant influence on the convergence rate of the solutions, and the numerical accuracy is relevant to the distance to the boundary where the local refinement acted; (3) as for the non-uniqueness problem, the imposition of specific interior boundary conditions not only obtains the best calculation result over the entire range of frequencies, but also has a simple integral formulation. • We implement an IGIBEM based on NURBS and PHT-splines for 3D acoustic problems. • The NURBS-based IBEM has super accuracy over the Lagrange-based IBEM. • The PHT-based IBEM was proposed to investigate the effect of local refinement on solution domain. • We investigated four indirect boundary integral equations to overcome the non-uniqueness problem. • The imposition of specific interior boundary conditions has simple integral formulation and the best calculation result.

The modified method of fundamental solutions for exterior problems of the Helmholtz equation; spurious eigenvalues and their removals

For the exterior Dirichlet problems (EDP) of the Helmholtz equation in 2D, when the Sommerfeld radiation condition is satisfied, there always exists the unique solution. Denote the unbounded domain S∞ outside of a bounded simply-connected domain, where the interior boundary Γin is non-circular. The standard MFS is first studied by using the complex Hankel function H0(1)(kr) as the fundamental solutions (FS). However, some solutions can not be obtained correctly (e.g., the spurious eigenvalues called). This paper is devoted to explore the spurious eigenvalues and their removals. For the non-circular interior boundary Γin, the error analysis is briefly made for the standard MFS, and some guidance is provided to bypass the spurious eigenvalues. Denote two nodes: P=(ρ,θ) and Q=(R,ϕ), and r=|PQ‾|=R2+ρ2−2Rρcos⁡(θ−ϕ). To completely eliminate all spurious eigenvalues, we solicit the new combined FS: (∂∂R±ik)H0(1)(kr) with i=−1, and propose the new modified MFS. The new algorithms are simple, and the strict analysis may be made. The bounds of errors are derived, and the polynomial convergence rates can be achieved. The bounds of condition numbers are derived for circular Γ∘in only, to display the exponential growth via the number of the new FS used. Numerical experiments are carried to support the analysis made. This paper is the first time for the MFS to explore the spurious eigenvalues and their removals, accompanied with strict analysis of errors and stability.

Bohmian Trajectories for Hamiltonians with Interior–Boundary Conditions

Recently, there has been progress in developing interior-boundary conditions (IBCs) as a technique of avoiding the problem of ultraviolet divergence in non-relativistic quantum field theories while treating space as a continuum and electrons as point particles. An IBC can be expressed in the particle-position representation of a Fock vector $\psi$ as a condition on the values of $\psi$ on the set of collision configurations, and the corresponding Hamiltonian is defined on a domain of vectors satisfying this condition. We describe here how Bohmian mechanics can be extended to this type of Hamiltonian. In fact, part of the development of IBCs was inspired by the Bohmian picture. Particle creation and annihilation correspond to jumps in configuration space; the annihilation is deterministic and occurs when two particles (of the appropriate species) meet, whereas the creation is stochastic and occurs at a rate dictated by the demand for the equivariance of the $|\psi|^2$ distribution, time reversal symmetry, and the Markov property. The process is closely related to processes known as Bell-type quantum field theories.

Three-Dimensional Simulation of Fluid–Structure Interaction Problems Using Monolithic Semi-Implicit Algorithm

A monolithic semi-implicit method is presented for three-dimensional simulation of fluid–structure interaction problems. The updated Lagrangian framework is used for the structure modeled by linear elasticity equation and, for the fluid governed by the Navier–Stokes equations, we employ the Arbitrary Lagrangian Eulerian method. We use a global mesh for the fluid–structure domain where the fluid–structure interface is an interior boundary. The continuity of velocity at the interface is automatically satisfied by using globally continuous finite element for the velocity in the fluid–structure mesh. The method is fast because we solve only a linear system at each time step. Three-dimensional numerical tests are presented.

Using an Experiment/Simulation-Integrated Approach To Investigate Fracture-Conductivity Evolution and Non-Darcy Flow in a Proppant-Supported Hydraulic Fracture

SummaryOptimizing proppant-pack conductivity in a hydraulic fracture is of critical importance to sustaining effective and economical production of petroleum hydrocarbons. In this study, a hybrid, experiment/simulation-integrated workflow, which combines the discrete element method (DEM) and the lattice Boltzmann (LB) method with laboratory-measured load-embedment correlations, was developed to advance the understanding of fracture-conductivity evolution from partial-monolayer to multilayer concentrations. The influence of compressive stress and proppant-diameter heterogeneity on non-Darcy flow behaviors was also investigated. The DEM method was used to simulate effective-stress increase and the resultant proppant-particle compaction and rearrangement. Proppant-embedment distance was then determined using an empirical correlation obtained by fitting experimental data. The final pore structure of the proppant pack was imported into the LB simulator as interior boundary conditions of fluid-flow modeling in the calculation of time-dependent permeability of the proppant pack. To validate the integrated workflow, proppant-pack conductivity as a function of increasing proppant concentration was simulated and then compared with laboratory data. Good agreement was observed between the workflow-derived and laboratory-measured fracture-conductivity vs. proppant-concentration curves. Furthermore, the role of proppant size, size heterogeneity, and closure pressure on the optimal partial-monolayer proppant concentration was investigated. The optimal partial-monolayer proppant concentration has important engineering implications, because one can achieve a considerable fracture conductivity using a partial-monolayer proppant structure, which has much lower material costs compared with the conventional multilayer proppant structures. To investigate the effect of non-Darcy flow on fracture conductivity, three proppant packs with the same average diameter but different diameter distributions were generated. Specifically, the coefficient of variation (COV) of diameter, defined as the ratio of standard deviation of diameter to mean diameter, was used to characterize the heterogeneity of particle size. The results of this research provide fundamental insights into the multiphysics processes regulating the conductivity evolution of a proppant-supported hydraulic fracture, as well as the role of compressive stress and proppant-size heterogeneity in non-Darcy flows.

Localized method of fundamental solutions for large-scale modelling of three-dimensional anisotropic heat conduction problems – Theory and MATLAB code

The method of fundamental solutions (MFS) belongs to the family of meshless boundary collocation methods and now has been successfully tried for many kinds of engineering problems. The traditional MFS based on the “global” boundary discretization, however, leads to dense and non-symmetric coefficient matrices that, although smaller in sizes, require huge computational cost to compute the system of equations using direct solvers. Such an approach will be arduous, time consuming and computationally expensive for analyzing large-scale problems. In the present work, a localized version of the MFS, named as the localized MFS (LMFS), is proposed for large-scale modelling of three-dimensional (3D) anisotropic heat conduction problems. In the LMFS, the computational domain can be divided into small subdomains with a simple geometry such as circle and/or sphere. To each of the subdomains, the MFS formulation is applied and the unknown coefficients on the local simple geometric boundary are approximated by the moving least square (MLS) method. The satisfactions of governing equations at interior points and boundary conditions at boundary nodes lead to a sparse and banded system matrix. Numerical examples with up to 1,000,000 unknowns are solved successfully using the developed LMFS code. The advantages, disadvantages and potential applications of the proposed method, as compared with the traditional MFS and boundary element method (BEM), are discussed. Finally, a fast, reliable and self-contained MATLAB code is provided in the part of Supplementary Materials of the paper.

Comprehensive study of the interactions between the critical dimensionless numbers associated with multiphase flow in 3D porous media

Multiphase flow in porous media is of great interest in many engineering applications, such as geologic carbon sequestration, enhanced oil recovery, and groundwater contamination and remediation. In order to advance the fundamental understanding of multiphase flow in complex three-dimensional (3D) porous media, the interactions between the critical dimensionless numbers, including the contact angle, viscosity ratio, and capillary (Ca) number, were investigated using X-ray micro-computed tomography (micro-CT) scanning and lattice Boltzmann (LB) modeling. In this study, the 3D pore structure information was extracted from micro-CT images and then used as interior boundary conditions of flow modeling in a pore-scale LB simulator to simulate multiphase flow within the pore space. A Berea sandstone sample was scanned and then two-phase flow LB simulations were performed based on the micro-CT images. The LB-simulated water/CO2 distributions agreed well with the micro-CT scanned images. Simulation results showed that a decreasing contact angle causes a decrease in wetting-fluid relative permeability and an increase in non-wetting fluid relative permeability. A rising Ca number increases both wetting and non-wetting fluid relative permeabilities. An increasing viscosity ratio (the ratio of non-wetting fluid viscosity to wetting fluid viscosity) facilitates the increase of non-wetting fluid relative permeability and mitigates the reduction of wetting fluid relative permeability, when the contact angle decreases continuously. The primary novel finding of this study is that the viscosity ratio affects the rate of change of the relative permeability curves for both phases when the contact angle changes continuously. To the best of our knowledge, it is the first time that comprehensive interactions between these dimensionless numbers are demonstrated in a sandstone sample based on real 3D structures. We also investigated the role of the changes of flow direction and sample location on relative permeability curves. Simulation results showed that the change in non-wetting fluid relative permeability was larger when the flow direction was switched from vertical to horizontal, which indicated that there was stronger anisotropy in larger pore networks that were primarily occupied by the non-wetting fluid.

Uniqueness of solution for plane deformations of a micropolar elastic solid with surface effects

We present a linear theory describing plane-strain deformations of a micropolar elastic solid which incorporates the additional contribution of surface micropolar elasticity. This theory provides a more comprehensive account of size effects in solids allowing for a more accurate representation of, for example, the mechanical properties of micro-/nanostructures. The surface model is represented by a thin micropolar reinforcing elastic shell of separate micropolar elasticity, perfectly bonded to the micropolar bulk and capable of both extension and bending. We present two different versions of the surface shell model: one which gives rise to a fourth-order surface theory and another which, via a particular form of the Kirchhoff–Love kinematic assumption, results in a second-order surface model. In each case, we formulate interior and exterior mixed boundary value problems and show that they can have at most one smooth solution despite the presence of boundary conditions of order equal to or higher than that of the governing equations. This result is essential in establishing that the corresponding mixed boundary value problems are well-posed in certain classes of smooth matrix functions.

Numerical Modeling of Hyperconcentrated Confluent Floods From the Middle Yellow and Lower Weihe Rivers

AbstractHyperconcentrated confluent floods in the Middle Yellow River and its tributaries are characterized by the phenomena of extremely high backwater stage, flood water intrusion, and local channel blockage in confluence areas. In order to study the propagation process of hyperconcentrated confluent floods, most existing channel network models need reinforcement in the computation of sediment transport and improvement in the treatment of interior boundary at channel junctions. A river network model for hyperconcentrated confluent floods is proposed based on the finite volume method scheme, in which the study domain is represented by ordinary 1‐D cells and junction cells. As a preprocess step, a bathymetry interpolation algorithm is developed to generate topography data and to extract the stage‐volume relationship for the junction cell. The storage change and sediment transport in the junction cell are calculated in each time step with no need to distinguish convergent or divergent flow pattern, and the solution in each reach can be executed simultaneously. The model was validated by simulating the hyperconcentrated confluent flood events in 1977 and 1966, with the maximum backwater stage and the occurrence time of flood water intrusion in the Lower Weihe River being well predicted. The response was investigated of the Middle Yellow River and Lower Weihe River to the arrangement of peak times of confluent floods, with the critical condition for flood water intrusion and the scenario that achieves the most effective scouring in the downstream channel being identified.

Effect of Size and Location of Square Web Openings on the Entire Behavior of Reinforced Concrete Deep Beams

This paper presents an experimental and numerical study which was carried out to examine the influence of the size and the layout of the web openings on the load carrying capacity and the serviceability of reinforced concrete deep beams. Five full-scale simply supported reinforced concrete deep beams with two large web openings created in shear regions were tested up to failure. The shear span to overall depth ratio was (1.1). Square openings were located symmetrically relative to the midspan section either at the midpoint or at the interior boundaries of the shear span. Two different side dimensions for the square openings were considered, mainly, (200) mm and (230) mm. The strength results proved that the shear capacity of the deep beam is governed by the size and location of web openings. The experimental results indicated that the reduction of the shear capacity may reach (66%). ABAQUS finite element software program was used for simulation and analysis. Numerical analyses provided un-conservative estimates for deep beam load carrying capacity in the range between (5-21%). However, the maximum scatter of the finite element method predictions for first diagonal and first flexural cracking loads was not exceeding (17%). Also, at service load the numerical of midspan deflection was greater than the experimental values by (9-18%).

Cavity identification in elastic structures by explicit domain mapping and boundary mode sensitivity analysis

This paper presents a novel cavity identification approach for linear elastic structures with the boundary mode data. The proposed approach consists of two major aspects. The first is the construction of an explicit domain mapping that maps the reference domain onto the physical domain by the level set functions. In proceeding so, the R-functions theory not only provide an analytical methodology to get the level set functions for the external and interior cavity boundaries, but also construct the desired domain mapping directly by level-set-functions weighted interpolation of the parameterized boundary mappings. The physical domain with the cavities is explicitly parameterized in the domain mapping and the desired mesh keeps fixed over the reference domain. The second is the enhanced sensitivity-based approach for minimum solution to the nonlinear least-squares goal function of the cavity identification problem. The sensitivity of the boundary modes to the geometric parameters is analyzed with the help of the acquired domain mapping and the trust-region constraint is introduced in order to reach a weak convergence. Numerical examples are conducted to show the feasibility and efficiency of the present cavity identification approach.

Localized method of fundamental solutions for solving two-dimensional Laplace and biharmonic equations

The localized method of fundamental solutions (LMFS) is proposed in this paper for solving two-dimensional boundary value problems, governed by Laplace and biharmonic equations, in complicated domains. Traditionally, the method of fundamental solutions (MFS) is a global method and the resultant matrix is dense and ill-conditioned. In this paper, it is the first time that the LMFS, the localized version of the MFS, is proposed. In the LMFS, the solutions at every interior node are expressed as linear combinations of solutions at some nearby nodes, while the numerical procedures of MFS are implemented within every local subdomain. The satisfactions of governing equation at interior nodes and boundary conditions at boundary nodes can yield a sparse system of linear algebraic equations, so the numerical solutions can be efficiently acquired by solving the resultant sparse system. Six numerical examples are given to demonstrate the effectiveness of the proposed LMFS.

Sb3+ and Gd3+ co-doped Cerium oxide Nanocrystalline Ceramic system: Structural and Dielectric Studies

Nanostructured ceramic materials have high conductivity compared to bulk materials. Ceria based systems, with fluorite structure, [samarium doped ceria (SDC) and gadolinium doped ceria (GDC)] are found to be the best electrolyte materials for intermediate temperature solid oxide fuel cells (IT-SOFC). In the present study, Ce0.8Gd0.1Sb0.1O2-δ nanostructured materials were synthesized by wet co-precipitation method. X ray diffraction pattern confirms the crystallization of the sample in the most conducting cubic fluorite phase. The presence of Ce, Gd, and Sb in the sample is qualitatively confirmed by Fourier transform infrared spectroscopy. Scanning electron spectroscopy image shows mesoporous nature of the sample. The addition of Sb3+ to the GDC system reduces the sintering temperature by 33.33%. The dielectric studies show that the prepared sample is an ionic material with two types of conduction mechanisms – grain interior and grain boundary. Hence, two different activation energies for ionic conduction are obtained for the sample at low and high temperature region.

Evaluative Case Study in Lightweight Wooden Wall Research

This presented article deals with two newly designed experimental walls with different measuring sections (5 for each lightweight wooden wall). All fragments meet the standards required for zero and energy-plus buildings, which would be mandatory in Slovakia from the year 2020. The experimental walls are located in central Europe (town Zilina, Slovakia). Description of individual test sections, the measuring technology, data collection, interior technical equipment and outdoor boundary conditions monitoring are introduced. In the future, the experimental research should progressively combine theoretical calculations with real measurement and computer HAM simulation. In this paper, the focus is aimed to the temperature profiles in wall fragments during seven days chosen from the spring period in the year 2017. The results were graphically presented and evaluated from a point of view of continuous temperature measurement in the structure, exterior boundary conditions, wall orientation and surface character (material, color). Also further intensions of research are drawn.

Роль и значение внутренних границ в магматической горной породе

Роль и значение внутренних границ в магматической горной породе

An electron-phonon coupling model for studying the effective thermal conductivity of nanocrystalline materials

The thermal conductivity of Nan crystalline materials has become one of the most advanced topics in international research. In this work, the effective thermal conductivity of NC materials based on the two-temperature model of heat conduction was studied. In the frame work of the developed model, we take the Nan crystalline materials as a composite materials composed by grain interior and grain boundary affect zone. The obtained analytical results showed that: (i) the thermal conductivity increases with the increasing of grain size with respect to the electron-phonon coupling length;

Optical, electrical properties and conduction mechanism of [(CH3)2NH2]2ZnCl4 compound

The hybrid compound Dimethylammonium zincochloride [(CH3)2NH2]2ZnCl4 is synthesized using a slow evaporation method at room temperature. It crystallizes in the monoclinic system with the P21/n space group. The differential scanning calorimetric shows one phase transition at 444 K. In optical studies, the analysis of the data revealed the existence of optical direct allowed transition mechanisms with the band gap energy equal to 4.26 eV. The ac electrical conductivity is investigated at the frequency and temperature range of 1 Hz–1 MHz and of 415 K–451 K respectively. The presence of the grain interior and grain boundary contributions to the electrical response in the material is clearly manifested in both of the two semicircles observed in the complex impedance. The equivalent circuit based on the Z-View-software is proposed and the conduction mechanisms are determined. Dielectric data are analyzed using complex electrical modulus M* at various temperatures.

Interactive effect of stress state and grain size on fracture behaviours of copper in micro-scaled plastic deformation

To explore the interactive influence of the deformation stress state and material microstructural grain size on the fracture behaviour in micro-scaled deformation, a series of micro-scale copper specimens of various geometrical dimensions and microstructural grain sizes are prepared and deformed to achieve various stress states represented by stress-related variables, such as the normalised third deviatoric stress invariant and the stress triaxiality. The speckle pattern method of continuous tracking is used to investigate the mechanical responses of materials in various deformation stress states and material microstructures, and a finite-element simulation of each deformation is conducted with the combined surface layer and grain boundary strengthening constitutive model, which considers the contributions of the surface grain, grain interior and grain boundary in representing the grain and geometry sizes. The interactive effects of the normalised third invariant, stress triaxiality and microstructural grain size on the fracture strain are identified and established by accounting for the correlation between the results of simulation and those of physical experimentation. Their influences on the fracture mechanism, mode and behaviour are further explored. The results reveal that greater stress decreases the fracture strain in the tensile deformation of round bar and cylindrical compression and increases the fracture strain in sheet shear and tensile deformations. The larger grain size generates fewer micro-voids, more uneven grain distribution and severer localisation deformation, which accelerates failure. Furthermore, stress triaxiality and the normalised third invariant at a low stress triaxiality are decreased with the increase of grain size, which in turn affects the occurrence of fracture. These effects coexist and compete with each other. In view of these influences, a larger grain size and a higher stress state inhibit the occurrence of fracture for sheet specimens with fracture modes from shear-dominant to dimple-dominant; in contrast, a smaller grain size and a lower stress state inhibit the occurrence of fracture in other cases.

Impeding effect of the Al3(Er,Zr,Li) particles on planar slip and intergranular fracture mechanism of Al-3Li-1Cu-0.1Zr-X alloys

The microstructure and mechanical properties of Al-3Li-1Cu-0.1Zr-xEr (x = 0, 0.1) alloys were investigated. With an addition of 0.1 wt% Er, dispersive core-shell structure Al3(Er,Zr,Li) particles were presented and the recrystallization was restrained. Besides, the trace of dislocations bypassing the Al3(Er,Zr,Li) particles was observed. Herein, the Orowan mechanism was also verified as the main strengthening mechanism of the Al3(Er,Zr,Li) particles by comparing the theoretical value in different strengthening mechanisms with the yield strength. The result demonstrated the impeding effect of the Al3(Er,Zr,Li) particles on the planar slip induced by shearing of the Al3Li, which also corresponded to the disappearance of the plastic instability in the alloy with Er addition. The Al-3Li-1Cu-0.1Zr-0.1Er alloy aged for 56 h possessed better ultimate tensile strength of 306 MPa and yield strength of 235 MPa. Interestingly, this alloy with unremarkable planar slip manifested lower elongation of 9.4% and obvious intergranular fracture when compared to the alloy without Er. To study this specific phenomenon, the hardness of grain interior and grain boundaries was investigated. The result showed that the intergranular fracture of this alloy was induced by higher strength of the grain interior than that of the grain boundaries, while the effect of the traditional planar slip mechanism was not apparent.

A New Non-Overlapping Domain Decomposition Method for a 3D Laplace Exterior Problem

We propose a method for solving three-dimensional boundary value problems for Laplace’s equation in an unbounded domain. It is based on non-overlapping decomposition of the exterior domain into two subdomains so that the initial problem is reduced to two subproblems, namely, exterior and interior boundary value problems on a sphere. To solve the exterior boundary value problem, we propose a singularity isolation method. To match the solutions on the interface between the subdomains (the sphere), we introduce a special operator equation approximated by a system of linear algebraic equations. This system is solved by iterative methods in Krylov subspaces. The performance of the method is illustrated by solving model problems.