Boundaries Of Arbitrary Shape Research Articles

Two-dimensional radial integration displacement discontinuity method with high-order isoparametric elements

To improve the accuracy of Displacement Discontinuity Method and enhance its adaptivity, a general-purpose two-dimensional displacement discontinuity method with both linear and quadratic isoparametric elements has been developed to model engineering discontinuity problems where cracks or cavities are involved. Linear and quadratic isoparametric elements have linear and quadratic distributions of displacement discontinuity, respectively. Both of them belong to the discontinuous element type, in which the geometry shape functions are different from the interpolation shape functions. A new general formulation, based on the boundary integral functions, is given for displacement discontinuity problems with arbitrary boundary shapes. This formulation contains singular and strongly singular integrals which can be evaluated in the sense of Cauchy principal value and Hadamard principal value, respectively. The radial integration technique is applied to perform these singular integrals with sufficiently high accuracy. Five numerical examples, most of which have analytic solutions, are given to illustrate the improved accuracy of the proposed approach. Compared with the constant displacement discontinuity element, the numerical results by using the present isoparametric displacement discontinuity elements show better accuracy.

Insights on using the boundary integral SPH formulations to calculate Laplacians with Dirichlet boundaries

Handling boundary conditions in Smooth Particle Hydrodynamics (SPH) has been known as a challenging problem for a long time, especially when particle approximation is implemented for truncated kernels on the boundary. This work develops a novel particle consistent gradient formulation to impose the Dirichlet boundary condition on a Laplacian with boundary integrals. Boundary integral formulation allows the accurate imposition of boundary conditions without creating virtual particles to extend boundaries, as used in conventional SPH modeling practices. Here, boundary integral formulations are presented for Laplacian operators and the imposition of Dirichlet boundary conditions on arbitrary boundary shapes. We also explore using this particle consistent first-order derivative twice to evaluate the entire Laplacian. Further, the convergence characteristics of different Laplacian formulations with boundary integrals are discussed. Finally, numerical experiments solving explicit thermal and fluid problems are presented to demonstrate the robustness of various Laplacian operators for practical use.

Numerical Modelling of Reactive Flows through Porous Media

We consider a lattice Boltzmann (LB) model to solve the coupled Navier–Stokes and advection–diffusion equation with reactive boundary conditions at the interface between fluid and solid domains. The reactive boundary condition results in the position of the boundary changing continuously, and so boundary nodes may be partially filled with fluid at any instant. We develop the LB boundary conditions for both the velocity and concentration fields in the presence of partially filled boundary nodes and then validate this algorithm on some test cases—the Stefan problem for diffusion-dominated dissolution and kinetic-dominated dissolution. It is shown that the developed model agrees well with analytic results, so that they can be used for more general boundaries of arbitrary shape. Numerical simulations in three dimensions are then carried out on demonstration problems at various Peclet numbers to elucidate the transport mechanisms and their influence on solid grain dissolution.

Pressure reconstruction of a planar turbulent flow field within a multiply connected domain with arbitrary boundary shapes

This paper reports for the first time the implementation procedures and validation results for pressure reconstruction of a planar turbulent flow field within a multiply connected domain that has arbitrary inner and outer boundary shapes. The pressure reconstruction algorithm used in this study is the rotating parallel-ray omni-directional integration algorithm that offers high-level of accuracy in the reconstructed pressure. While preserving the nature and advantage of the parallel ray omni-directional pressure reconstruction at places with flow data, the new implementation of the algorithm is capable of processing an arbitrary number of inner void areas with arbitrary boundary shapes. Validation of the multiply connected domain pressure reconstruction code is conducted using the Johns Hopkins DNS (Direct Numerical Simulation) isotropic turbulence databases [J. Graham et al., J. Turbul. 17(2), 181 (2016)], with 1000 statistically independent pressure gradient field realizations embedded with random noise used to gauge the code performance. For further validation, the code is also applied for pressure reconstruction from the DNS data [E. Johnsen and T. Colonius, J. Fluid Mech., 629, 231 (2009)] about a shock-induced non-spherical bubble collapse in water. It is demonstrated that the parallel-ray omni-directional integration algorithm outperforms the Poisson equation approach in terms of the accuracy for the pressure reconstruction from error embedded pressure gradients in both simply connected and multiply connected domains.

A Bayesian Approach to the Data Description Problem

In this paper, we address the problem of data description using a Bayesian framework. The goal of data description is to draw a boundary around objects of a certain class of interest to discriminate that class from the rest of the feature space. Data description is also known as one-class learning and has a wide range of applications. The proposed approach uses a Bayesian framework to precisely compute the class boundary and therefore can utilize domain information in form of prior knowledge in the framework. It can also operate in the kernel space and therefore recognize arbitrary boundary shapes. Moreover, the proposed method can utilize unlabeled data in order to improve accuracy of discrimination. We evaluate our method using various real-world datasets and compare it with other state of the art approaches of data description. Experiments show promising results and improved performance over other data description and one-class learning algorithms.

Pressure reconstruction of a planar turbulent flow field within a multiply-connected domain with arbitrary boundary shapes

Over the past two decades, it has been demonstrated that the instantaneous spatial pressure distribution in a turbulent flow field can be reconstructed from the pressure gradient field non-intrusively measured by Particle Image Velocimetry (PIV). Representative pressure reconstruction methods include the omnidirectional integration (Liu and Katz, 2006; Liu et al., 2016; Liu and Moreto, 2020), the Poisson equation approach (Violato et al., 2011; De Kat and Van Oudheusden, 2012), the least-square method (Jeon et al., 2015), and most recently, the adjoint-based sequential data assimilation method, which also essentially utilizes the Poisson equation to reconstruct the pressure(He et al., 2020). Most of these previous pressure reconstruction examples, however, were applied to simply-connected domains (Gluzman et al., 2017) only. None of these previous studies have discussed how to apply the pressure reconstruction procedures to a multiply-connected domain (Gluzman et al., 2017). To fill in this gap, this paper presents a detailed report for the first time documenting the implementation procedures and validation results for pressure reconstruction of a planar turbulent flow field within a multiply-connected domain that has arbitrary inner and outer boundary shapes. The pressure reconstruction algorithm used in the current study is the rotating parallelray omni-directional integration algorithm, which, as demonstrated in reference (Liu and Moreto, 2020) based on simply-connected flow domains, offers high-level of accuracy in the reconstructed pressure. While preserving the nature and advantage of the parallel ray omni-directional pressure reconstruction at places with flow data, the new implementation of the algorithm is capable of processing an arbitrary number of inner void areas with arbitrary boundary shapes. Validation of the multiply-connected domain pressure reconstruction code is conducted using the DNS (Direct Numerical Simulation) isotropic turbulence field available at the Johns Hopkins Turbulence Databases, with 1000 statistically independent pressure gradient field realizations embedded with random noise used to gauge the code performance. For further validation, the code is also applied for pressure reconstruction from the DNS pressure gradient in the ambient flow field of a shock-induced non-spherical bubble collapse in water (Johnsen and Colonius, 2009). The successful implementation of the parallel ray pressure reconstruction method to multiply-connected domains paves the way for a variety of important applications including, for example, experimental characterization of pressure field changes during the process of cavitation bubble inception, growth and collapse, non-intrusive unsteady aerodynamic force assessment for an arbitrary body shape immersed in flows, and multi-phase flow investigations, etc. In particular, as an immediate follow-up effort, the parallel ray pressure code will be used for the instantaneous pressure distribution reconstruction of the turbulent flow surrounding cavitation inception bubbles occurring on top of a cavity trailing corner based on high-speed PIV measurements.

Structural Morphogenesis for RC Free-Form Surface Shell with Arbitrary Boundary Shape And Opening - Comparison of Optimal Solution and Application of Decent Solutions Search Method

In this paper, artificial bee colony (ABC) to obtain the decent solutions that the authors proposed is applied to the structural morphogenesis for RC (Reinforced-Concrete) free-form surface shell with arbitrary boundary shape. The 'decent solutions' have relatively high evaluation solutions that maintain the diversity of the design variable space, including the global optimal solution and local optimal solutions. In this paper, we focus on an opening of RC free form surface shell structures considering design and functionality, and the structural morphogenesis procedure that considers constraints of the excessive bending moment caused by the presence of an opening in the shell is proposed. Numerical results demonstrate the efficacy of a structural morphogenesis procedure that simultaneously considers shell shape, thickness, and opening as design variables. Furthermore, it is shown that proposed structural morphogenesis using decent solutions search method can support a designer's idea of architectural forms having a relationship between shape and mechanical behavior at the initial stage of design.

Evaluation of transient pressure responses of a hydraulically fractured horizontal well in a tight reservoir with an arbitrary shape by considering stress-sensitive effect

In this study, a semianalytical technique has been developed to examine stress-sensitive effect on the transient pressure responses of a multiple-fractured horizontal well in an unconventional reservoir with an arbitrary-shape. Considering its arbitrary-shaped boundaries, the boundary element method is adopted to simulate flow behaviour by incorporating the permeability modulus (i.e., stress-sensitive effect) into the governing equation to describe the flow behaviour within the hydraulic fractures. To weaken the nonlinearity of such governing equations in a hydraulic fracture subsystem, a semianalytical approach is used to achieve consistent solutions with good accuracy. The convergence skin effect is introduced to represent the radial fluid-flow pattern in the hydraulic fractures near the horizontal wellbore. Not only can the stress-sensitive effects of hydraulic fractures be examined, but also the corresponding pressure responses together with pressure derivative curves are obtained. The mathematical formulations have been verified and then extended for field applications. The stress-sensitive effect of hydraulic fractures in a box-shaped reservoir with closed boundaries is found to be obvious during the intermediate- and late-time periods. Furthermore, the noticeable stress-sensitive effect in hydraulic fractures occurs earlier by taking the convergence-skin effect into account. A hydraulic fracture with a high permeability modulus is found to result in a positive stress-sensitive effect. Also, sensitivity analysis on pressure responses and their corresponding derivative curves have been performed with respect to the convergence skin effect, boundary shape, maximum distance, and minimum fracture conductivity.

A generalized complex variable method for multiple tunnels at great depth considering the interaction between linings and surrounding rock

The mechanical analysis of multiple tunnels at great depth is an extremely common problem in practical engineering. Previous studies usually used the Schwarz alternating method to solve the multiple-tunnel problem with an iterative scheme, which resulted in low efficiency and precision. To this end, this paper presents a non-iterative analytical method to calculate the mechanical field of multiple lined tunnels. In this method, the analytic function is expanded by Laurent series on each tunnel boundary so that the stress and displacement fields in the whole multiply-connected domain can be expressed accurately. The conformal mappings of different tunnels are independent of each other, which makes it convenient to deal with multiple arbitrary-shaped boundaries. The basic equations for solving the mechanical fields are obtained according to the contact conditions and stress boundary conditions. In the solving process, the Fourier transform method is used to transform the boundary conditions into the frequency equations. Compared with the Schwarz alternating method, our method can directly obtain the high-quality result without any iteration. Finally, several examples are given to verify the accuracy and effectiveness of the proposed method.

Parallel implementation of a VIScous Vorticity Equation (VISVE) method in 3-D laminar flow

This paper presents a newly developed parallel implementation of solving the 3–D vorticity equation to fully simulate the incompressible laminar flow in the Eulerian frame. This method is designed to solve 3–D problems with irregular wall boundaries in small and compact computational domains in general shapes efficiently. The curl form of vorticity equation is discretized using the Finite Volume Method (FVM) by applying Stokes' theorem, which automatically guarantees the divergence–free condition of vorticity field at all times. The vorticity preserving velocity field is recovered by an explicit scheme without solving any linear system, and this velocity field is reprojected onto a divergence–free space by solving only one scalar velocity–potential Poisson's equation. The vorticity boundary condition is satisfied by employing a vorticity creation scheme, that can handle arbitrary wall boundary shapes. Numerical results of the flow past a 3–D NACA0012 hydrofoil with one periodic direction, the flow past a sphere, and the flow past a 3–D rectangular wing are presented to validate the scheme.

Adaptive Developmental Resonance Network.

Adaptive resonance theory (ART) networks, including developmental resonance network (DRN), basically use a vigilance parameter as a hyperparameter to determine whether a current input can belong to any existing categories or not. The problem here is that the clustering quality of those networks is sensitive to the vigilance parameter so that the users are required to fine-tune the parameter delicately beforehand. Another problem is that those networks only deal with a hyperrectangular decision boundary, which means they cannot learn categories of arbitrary shape. In addition, the order of data processing is a critical factor to categorize clusters correctly because each category can expand its boundary into the areas of other categories erroneously. To deal with these problems, we propose an advanced version of DRN, Adaptive DRN (A-DRN), which learns the vigilance parameters assigned for individual category nodes as well as category weights. The proposed A-DRN combines close categories to construct a cluster that contains the categories identifying a cluster boundary of arbitrary shape. Our A-DRN also employs a sliding window. The sliding window buffers sequential data points to presume the data distribution roughly, which helps our network to have a robust and consistent performance to a random order of input data. Through the experiments, we empirically demonstrate the effectiveness of A-DRN in both synthetic and real-world benchmark data sets.

Design of a neutral elastic inhomogeneity via thermal expansion

A neutral elastic inhomogeneity does not affect the existing stress field when inserted into an elastic body. It has been shown that no such inhomogeneity can exist under the classical assumption of a perfectly bonded interface between the inhomogeneity and the surrounding material. We show that by introducing a suitable temperature field inside the inhomogeneity it is indeed possible to achieve neutrality regardless of the perfect bonding assumption. Specifically, we show that a nonuniform internal temperature field can induce neutrality in an inhomogeneity in the form of an elastic ring with concentric internal and external boundaries of arbitrary shape. Noting that such a temperature field can be identified also in the case of an unpunched inhomogeneity when the inhomogeneity is line-shaped, we further prove that even a flake-shaped inhomogeneity can be made neutral if the thickness of the flake is much smaller than its length. In the case that the elastic body surrounding the unpunched inhomogeneity is subjected to remote hydrostatic loading, the temperature field within the inhomogeneity will remain uniform and independent of the shape of the inhomogeneity. In fact, in this case, the temperature field inside the inhomogeneity depends only on the elastic parameters of the composite and the direction of the remote loading and can be higher or lower than the operating temperature of the composite.

Numerical simulation of a drop impact on a superhydrophobic surface with a wire

Superhydrophobic surfaces patterned with macroscale (≈1 mm) structures have gained increasing interest in the past years because of their potential in reducing the contact time between impacting liquid drops and the solid surface. The reduced wettability of these surfaces is of interest in numerous technical applications, as, for example, in anti-icing on airplane wings. Several experimental studies have been carried out on this topic in the literature; on the other hand, only very limited numerical investigations are available in the literature. In this paper, we present a numerical study based on a volume of fluid code for direct numerical simulation of incompressible multiphase flows. A necessary condition for the realization of this study was the implementation of arbitrary-shaped boundaries using a Cartesian grid system. Our implementation of embedded boundaries is based on a volume fraction representation of the boundaries and on a piecewise linear approximation of their surface. The discretized boundaries are then cut off from the computational domain, leading to an altered formulation of the discretized governing equations. To validate the method, we show simulation results for different impact velocities for the case of a droplet impacting on a wire, which has been investigated experimentally in the literature. The simulations show good agreement in terms of contact time and impact morphology, thus, showing the validity of the implementation. Moreover, an extensive analysis of the velocity field for this setup is presented, helping us to better understand the underlying physical phenomena.

Quantitative detection of internal defects based on morphological opening, filling and binarizing operations on wrapped phase of out-of-plane deformation in digital speckle pattern interferometry

A novel method used for quantitative detection of internal defects with boundary of arbitrary shape is proposed in this paper for the first time. This method can be used to determine accurately the location and size of internal defects based on sequential morphological opening, filling and binarizing operations on the wrapped phase of out-of-plane deformation in phase-shifting digital speckle pattern interferometry. Because internal defects are detected directly from a wrapped phase rather than an unwrapped phase, the method proposed in this paper requires neither unwrapping of wrapped phase nor denoising of interference fringes when used for quantitative detection of internal defects. Theoretical analysis, numerical simulation, experimental verification and error calculation are presented in this paper.

A New Design of Electrical Impedance Tomography Sensor System for Pulmonary Disease Diagnosis

AbstractAs an advanced process detection technology, electrical impedance tomography (EIT) has wide application prospects and advantages in medical imaging diagnosis. However, a series of issues need to be addressed before applying EIT for bedside monitoring. Medical diagnosis and bedside monitoring are dynamic measuring process, where the positions of measuring electrodes and the shape of the detected field are changing dynamical. Due to the inability to cope with the changeable electrode positions and various dynamic fields, existing EIT systems are mainly used for industrial detection in condition of static measurement and visualization. In this paper, we investigate the dynamic measurement and visualization of human breast in EIT field, describe the design of the measuring sensor system, and expound the measuring principle. The main component of the hardware system is a built-in servo electrical resistance tomography sensor with capacitive sliding rod, which can adapt to the crowd of different chest contour and the change of chest shape in the dynamic process of breathing. The corresponding measuring principle is extracting all real-time positions of measuring electrodes, then obtaining the dynamic boundary, finally dividing the detection field rapidly. Experimental results confirmed that the proposed system can obtain real-time location of boundary sensor and dynamically solve the problem of arbitrary-shape boundary measurement. The imaging results validate the availability of designed sensor system and the effectiveness of the corresponding measuring principle.

Energy storage in a complex heat storage unit using commercial grade phase change materials: Effect of convective heat transfer boundary conditions

For the storage of latent energy in an arbitrary-shaped double-pipe heat exchanger is considered in this study. The heat exchanger is numerically modeled considering the convective heat transfer boundary condition on the inner tube. The horizontal heat exchanger is composed of an insulated outer hexagonal tube and an inner tube. The commercial grade PCM which melts over a temperature range of 8.7 °C is placed in the annular gap between the two tubes. The flow rate and the inlet temperature of the heat transfer fluid (HTF) flowing through the inner tube are varied for the low-temperature solar energy storage. The cross-sectional shapes of the inner tube as well as the vertical position of the circular tube are varied, keeping the cross-sectional area of the annular gap constant. In order to correctly account for the arbitrary-shaped boundaries, a non-orthogonal boundary-fitted coordinate technique on a staggered grid system is used. A control volume based finite difference scheme is employed to solve the non-dimensional set of equations. The predicted results of the velocity and temperature fields, the surface-averaged Nusselt number on the heat transfer surface of the inner tube, the complete and total melt fractions, and the latent and total cumulative energy stored, all as a function of time are presented and discussed. The results show that the effect of the change of the bulk temperature is much more prominent on the storage of energy compared to the change in the mass flow rate of the HTF. For the identical conditions, the oblate-shaped inner tube stores the maximum amount of energy irrespective of the studied shapes and the vertical positions of the inner tube.

Satellite Radiothermovision on Synoptic and Climatically Significant Scales

This paper is focused on the development of a methodological basis for the authors’ approach to the processing of large volumes of satellite radiothermal data, which is known as satellite radiothermovision. A closed scheme for calculating the latent heat flux (and other integral characteristics of the dynamics of geophysical fields) through arbitrary contours (boundaries) has been constructed and mathematically described. The opportunity for working with static, as well as movable and deformable boundaries of arbitrary shape, has been provided. The computational scheme was tested using the example of calculations of the atmospheric advection of the latent heat from the North Atlantics to the Arctic in 2014. Preliminary analysis of the results showed a high potential of the approach when applying it to the study of a wide range of synoptic and climatically significant atmospheric processes of the Earth. Some areas for the further development of the satellite radiothermovision approach are briefly discussed. It is noted that expanding the analysis of the available satellite data to as much data as possible is of considerable importance. Among the immediate prospects is the analysis of large arrays of data already accumulated and processed in terms of the satellite radiothermovision ideology, which are partially presented and continuously updated on a specialized geoportal.

Dirichlet boundary conditions for arbitrary-shaped boundaries in stellarator-like magnetic fields for the Flux-Coordinate Independent method

We present a technique for handling Dirichlet boundary conditions with the Flux Coordinate Independent (FCI) parallel derivative operator with arbitrary-shaped material geometry in general 3D magnetic fields. The FCI method constructs a finite difference scheme for ∇∥ by following field lines between poloidal planes and interpolating within planes. Doing so removes the need for field-aligned coordinate systems that suffer from singularities in the metric tensor at null points in the magnetic field (or equivalently, when q→∞). One cost of this method is that as the field lines are not on the mesh, they may leave the domain at any point between neighbouring planes, complicating the application of boundary conditions.The Leg Value Fill (LVF) boundary condition scheme presented here involves an extrapolation/interpolation of the boundary value onto the field line end point. The usual finite difference scheme can then be used unmodified. We implement the LVF scheme in BOUT++ and use the Method of Manufactured Solutions to verify the implementation in a rectangular domain, and show that it does not modify the error scaling of the finite difference scheme. The use of LVF for arbitrary wall geometry is outlined.We also demonstrate the feasibility of using the FCI approach in non-axisymmetric configurations for a simple diffusion model in a “straight stellarator” magnetic field. A Gaussian blob diffuses along the field lines, tracing out flux surfaces. Dirichlet boundary conditions impose a last closed flux surface (LCFS) that confines the density. Including a poloidal limiter moves the LCFS to a smaller radius.The expected scaling of the numerical perpendicular diffusion, which is a consequence of the FCI method, in stellarator-like geometry is recovered. A novel technique for increasing the parallel resolution during post-processing, in order to reduce artefacts in visualisations, is described.

An overview of boundary implementation in lattice Boltzmann method for computational heat and mass transfer

The ability to deal with the complex geometries precisely and accurately has always been the most integral part of any computational fluid dynamics approach. The lattice Boltzmann method has already achieved considerable success in the simulation of unsteady flow with arbitrary boundary shapes. To include boundaries in the lattice Boltzmann simulations, several methods have been presented in the past to satisfy the standard boundary implementation of macroscopic flows. In spite of the considerably vast body of literatures that discuss in this field, the study still is in progress. The current study is an overview of the adopted boundary conditions in lattice Boltzmann method.

Adaption for 2-D Edge Elements in the Nonconforming Voxel Finite-Element Method

The nonconforming voxel finite-element (FE) method avoids many of the difficulties of traditional FE mesh generation using a nested grid of rectangular elements. It models arbitrary boundary shapes by adaptively refining the mesh at the boundaries. Here, the adaption is extended to reduce errors arising from elements that are away from boundaries, but are too big to represent the field adequately. The application is to 2-D edge elements for solving the time-harmonic wave equation. Results for a miter-bend waveguide and a dielectric post resonator demonstrate the effectiveness of the new algorithm.