Interior Boundary Conditions Research Articles

Analysis of three-dimensional interior acoustic fields by using the localized method of fundamental solutions

• Applying the localized method of fundamental solutions for 3D interior acoustic fields. • The behavior of the present method for oscillating solution is first investigated. • Acoustic fields in a high-speed train and a room with complicated geometries are solved successfully. The traditional method of fundamental solutions has a full interpolation matrix, and thus its solution is computationally expensive, especially for large-scale problems with complicated domains. In this paper, we make a first attempt to apply the localized method of fundamental solutions for analysis of 3D interior acoustic fields. The present method first divides the whole computational domain into some overlapping subdomains, and then expresses physical variables as linear combinations of the fundamental solution in each subdomain. Finally, the method forms a sparse and banded system matrix by satisfying both governing equations at interior nodes and boundary conditions at boundary nodes. We provide four numerical experiments to verify the accuracy and the stability of the method. Comparisons of numerical results and computational time are also made between the present method, the method of fundamental solutions, and the COMSOL software.

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.

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.

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.

Complex charges, time reversal asymmetry, and interior-boundary conditions in quantum field theory

While fundamental physically realistic Hamiltonians should be invariant under time reversal, time asymmetric Hamiltonians can occur as mathematical possibilities or effective Hamiltonians. Here, we study conditions under which non-relativistic Hamiltonians involving particle creation and annihilation, as come up in quantum field theory (QFT), are time asymmetric. It turns out that the time reversal operator T can be more complicated than just complex conjugation, which leads to the question which criteria determine the correct action of time reversal. We use Bohmian trajectories for this purpose and show that time reversal symmetry can be broken when charges are permitted to be complex numbers, where ‘charge’ means the coupling constant in a QFT that governs the strength with which a fermion emits and absorbs bosons. We pay particular attention to the technique for defining Hamiltonians with particle creation based on interior-boundary conditions, and we find them to generically be time asymmetric. Specifically, we show that time asymmetry for complex charges occurs whenever not all charges have equal or opposite phase. We further show that, in this case, the corresponding ground states can have non-zero probability currents, and we determine the effective potential between fermions of complex charge.

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.

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.

An innovative PCM system for thermal comfort improvement and energy demand reduction in building under different climate conditions

In recent years, applying phase change materials (PCMs) has attracted growing attention due to its potential to energy conservation with thermal comfort in the buildings. The proper use of PCM in a building can reduce the energy demand considerably, keeping the indoor temperature within the comfort range. One of the major issues associated with the use of PCM is the dependency of its performance on the climate conditions, such as the ambient temperature in which it is used. This study introduces an innovative double layer PCM system aim to improve thermal comfort conditions and minimize energy demand. In the scope of PCM performance improvement under different climates during hot and cold months, a constructive solution is the incorporation of two PCM types with different properties, such as melting temperature and enthalpy in room envelopes. The behavior of such a system under five different climatic regions with emphasis on dry and semi-arid climates as dominant climates of Iran was numerically investigated. The study of this new system is conducted by a room with one exterior and some interior boundary conditions in hot and cold months. In this work, The Fanger comfort model has been used for a comprehensive evaluation of new system’s impact on thermal comfort conditions. The results showed that the double layer PCM system improves percentage of time in which the indoor thermal comfort conditions are met from 73% to 93% in dry climate, and from 63% to 75% in semi-arid climate in winter. Furthermore, the heating energy consumption is reduced by 17.5% in dry climate, and by 10.4% in semi-arid climate in the country of Iran.

Spectral distribution problem for Sturm-Liouville with operators the discontinuity conditions at an interior point and boundary conditions depending on the eigenparameter

Spectral distribution problem for Sturm-Liouville with operators the discontinuity conditions at an interior point and boundary conditions depending on the eigenparameter

Comparative 1D and 3D numerical investigation of open-channel junction flows and energy losses

Abstract The complexity of open channel confluences stems from flow mixing, secondary circulation, post-confluence flow separation, contraction and backwater effects. These effects in turn result in a large number of parameters required to adequately quantify the junction induced hydraulic resistance and describe mean flow pattern and turbulent flow structures due to flow merging. The recent development in computing power advances the application of 3D Computational Fluid Dynamics (CFD) codes to visualize and understand the Confluence Hydrodynamic Zone (CHZ). Nevertheless, 1D approaches remain the mainstay in large drainage network or waterway system modeling considering computational efficiency and data availability. This paper presents (i) a modified 1D nonlinear dynamic model; (ii) a fully 3D non-hydrostatic, Reynolds-averaged Navier–Stokes Equations (RANS)-based, Computational Fluid Dynamics (CFD) model; (iii) an analysis of changing confluence hydrodynamics and 3D turbulent flow structure under various controls; (iv) a comparison of flow features (i.e. upstream water depths, energy losses and post-confluence contraction) predicted by 1D and 3D models; and (v) parameterization of 3D flow characteristics in 1D modeling through the computation of correction coefficients associated with contraction, energy and momentum. The present comprehensive 3D numerical investigation highlights the driving mechanisms for junction induced energy losses. Moreover, the comparative 1D and 3D study quantifies the deviation of 1D approximations and associated underlying assumptions from the ‘true’ resultant flow field. The study may also shed light on improving the accuracy of the 1D large network modeling through the parameterization of the complex 3D feature of the flow field and correction of interior boundary conditions at junctions of larger angles and/or with substantial lateral inflows. Moreover, the enclosed numerical investigations may enhance the understanding of the primary mechanisms contributing to hydraulic structure induced turbulent flow behavior and increased hydraulic resistance.

Particle Creation at a Point Source by Means of Interior-Boundary Conditions

We consider a way of defining quantum Hamiltonians involving particle creation and annihilation based on an interior-boundary condition (IBC) on the wave function, where the wave function is the particle-position representation of a vector in Fock space, and the IBC relates (essentially) the values of the wave function at any two configurations that differ only by the creation of a particle. Here we prove, for a model of particle creation at one or more point sources using the Laplace operator as the free Hamiltonian, that a Hamiltonian can indeed be rigorously defined in this way without the need for any ultraviolet regularization, and that it is self-adjoint. We prove further that introducing an ultraviolet cut-off (thus smearing out particles over a positive radius) and applying a certain known renormalization procedure (taking the limit of removing the cut-off while subtracting a constant that tends to infinity) yields, up to addition of a finite constant, the Hamiltonian defined by the IBC.

Non-CMC Solutions of the Einstein Constraint Equations on Compact Manifolds with Apparent Horizon Boundaries

In this article we continue our effort to do a systematic development of the solution theory for conformal formulations of the Einstein constraint equations on compact manifolds with boundary. By building in a natural way on our recent work in Holst and Tsogtgerel (2013), and Holst, Nagy, and Tsogtgerel (2008, 2009), and also on the work of Maxwell (2004, 2005, 2009) and Dain (2004), under reasonable assumptions on the data we prove existence of both near- and far-from-constant mean curvature solutions for a class of Robin boundary conditions commonly used in the literature for modeling black holes, with a third existence result for constant mean curvature (CMC) appearing as a special case. Dain and Maxwell addressed initial data engineering for space-times that evolve to contain black holes, determining solutions to the conformal formulation on an asymptotically Euclidean manifold in the CMC setting, with interior boundary conditions representing excised interior black hole regions. Holst and Tsogtgerel compiled the interior boundary results covered by Dain and Maxwell, and then developed general interior conditions to model the apparent horizon boundary conditions of Dain and Maxwell for compact manifolds with boundary, and subsequently proved existence of solutions to the Lichnerowicz equation on compact manifolds with such boundary conditions. This paper picks up where Holst and Tsogtgerel left off, addressing the general non-CMC case for compact manifolds with boundary. As in our previous articles, our focus here is again on low regularity data and on the interaction between different types of boundary conditions. While our work here serves primarily to extend the solution theory for the compact with boundary case, we also develop several technical tools that have potential for use with the asymptotically Euclidean case.

A simplified dynamic zone model for a probabilistic assessment of hygrothermal risks in building components

Most building component simulation software simplify the interior boundary conditions; only the temperature and relative humidity can be assigned. However, when performing a probabilistic assessment of the hygrothermal risks, a wider range of realistic indoor boundary conditions can be desired, and more indoor climate parameters need to be implemented. Instead of combining with a complex BES-model, an integrated simplified dynamic zone model is proposed, developed to expand the functionality of DELPHIN 5.8. In this zone model, the original interior boundary conditions are replaced by a fictive air layer, representing the indoor zone and thus the indoor conditions to which the building component is exposed. The air layer, in turn, is subjected to equivalent boundary conditions. Through these equivalent boundary conditions and air layer properties, the indoor climate parameters are taken into account. Hence, this model enables to assess a broader variety of interior climates.

Intention, Principle, Outputs and Aims of the Experimental Pavilion Research of Building Envelopes Including Windows for Wooden Buildings

Abstract The aim of experimental research in the area of exterior walls and windows suitable for wooden buildings was to build special pavilion laboratories. These laboratories are ideally isolated from the surrounding environment, airtight and controlled by the constant internal climate. The principle of experimental research is measuring and recording of required physical parameters (e.g. temperature or relative humidity). This is done in layers of experimental fragment sections in the direction from exterior to interior, as well as in critical places by stable interior and real exterior climatic conditions. The outputs are evaluations of experimental structures behaviour during the specified time period, possibly during the whole year by stable interior and real exterior boundary conditions. The main aim of this experimental research is processing of long-term measurements of experimental structures and the subsequent analysis. The next part of the research consists of collecting measurements obtained with assistance of the experimental detached weather station, analysis, evaluation for later setting up of reference data set for the research locality, from the point of view of its comparison to the data sets from Slovak Hydrometeorological Institute (SHMU) and to localities with similar climate conditions. Later on, the data sets could lead to recommendations for design of wooden buildings.

Particle creation and annihilation at interior boundaries: one-dimensional models

We describe creation and annihilation of particles at external sources in one spatial dimension in terms of interior-boundary conditions (IBCs). We derive explicit solutions for spectra, (generalised) eigenfunctions, as well as Green functions, spectral determinants, and integrated spectral densities. Moreover, we introduce a quantum graph version of IBC-Hamiltonians.

Phase change material's (PCM) impacts on the energy performance and thermal comfort of buildings in a mild climate

The current residential buildings are of light weight construction. As such, they tend to frequent indoor air temperatures fluctuations and have been proven detrimental for thermal comfort and mechanical system energy consumption. This is reflected in the energy consumption statistics for residential buildings. More than 62% of the building energy use is towards maintaining comfortable indoor conditions. Phase change materials (PCM); a latent heat thermal storage material, have the potential to increase the thermal mass of these buildings without drastically affecting the current construction techniques. In this paper, the potential of phase change materials is investigated through numerical and experimental studies. The field experimental study is conducted using twin side-by-side buildings exposed to the same interior and exterior boundary conditions, and EnergyPlus, after being benchmarked with the experimental results, is used for the numerical study. The numerical study is carried out for an existing residential apartment unit with particular emphasis on the effects of different design parameters such as orientation and window to wall ratio. Preliminary analyses of experimental data show that phase change materials are effective in stabilizing the indoor air by reversing the heat flow direction. In fact, the indoor air and wall temperature fluctuations are reduced by 1.4 °C and 2.7 °C respectively. Following, benchmarking of the numerical simulation shows confidence levels in predicting the interior conditions since discrepancies between experimental data and numerical data are within tolerance limits of the measuring device. Further, from the analysis of the numerical data, phase change material is effective in moderating the operative temperature but does not translate to significant thermal comfort improvement when evaluated over a night time occupancy regime in the summer. On the contrary, PCM is effective in lowering the heating energy demand by up to 57% during the winter condition.

A discontinuous Galerkin method for modeling flow in networks of channels

Flow in a network of numerous channels is a complex phenomenon that cannot be adequately modeled by 1-D models. Despite this, it is a common practice to model flow in each channel with the 1-D St. Venant equations. These channels are coupled with each other by prescribing some interior boundary conditions, which are either too simplistic to reproduce the physics accurately or are computationally expensive. In this paper, we present a dimensionally heterogeneous approach to resolve these issues. We treat flows in individual channels as 1-D flows. These channels are coupled together at junctions using a 2-D junction region. We present a systematic numerical treatment of the 1-D and the 2-D shallow water equations in the framework of an RKDG method so that the coupling between the 1-D and the 2-D domains is natural, conservative and consistent with the numerical scheme. We verify the 1-D and the 2-D code via comparisons with different analytical solutions for a wide variety of cases. We establish the accuracy of our heterogeneous junction model by comparing the simulation results to experimental data and to the results obtained from other junction models.

Numerical evaluation of a phase change material–shutter using solar energy for winter nighttime indoor heating

The incorporation of phase change materials in movable structural cells of shading elements associated with southward-facade windows is evaluated in this article. The proposed phase change material–shutter is a thermal energy storage system designed to take advantage of solar energy for winter nighttime indoor heating. A two-dimensional phase-change heat diffusion model based on the enthalpy formulation was considered. The numerical model follows the finite-volume method with a fully implicit formulation and allows the alternating melting and solidification of a phase change material submitted to cyclical thermal boundary conditions. Parametric investigations were carried out about the effects of thermophysical properties of the phase change material and temperature and convection heat transfer boundary conditions on the charge/discharge rates of energy. Due to the low thermal diffusivity of the phase change material, an aluminum fin arrangement was considered as a heat transfer enhancement technique. The distance between fins is directly proportional to the daily energy storage/release capacity of the system. The solar radiation flux has a strong effect on the charging/melting processes during the day. The indoor temperature and the interior convection heat transfer coefficient have a major influence on the discharging/freezing processes during the night. The design of the phase change material–shutter depends strongly on the thermophysical properties of the phase change material and on the interior and exterior boundary conditions considered.