Boundary Nodes Research Articles

Hybrid absorbing boundary condition for piecewise smooth curved boundary in 2D acoustic finite difference modelling

Flexible computational domains and their corresponding irregular absorbing boundary conditions (ABCs) have previously been shown to improve the efficiency of finite difference (FD) modelling. However, these proposed ABCs for irregular boundaries are based on irregular grid methods. Although they can improve geometric flexibility of FD modelling, irregular grid methods are still complex to implement due to computationally expensive meshing process. To avoid complex mesh generation, FDs in mesh-free discretisation have been developed for nontrivial geometric settings, where scattered nodes can be placed suitably with respect to irregular boundaries and arbitrarily shaped anomalies without coordinate mapping or mesh-element forming. Radial-basis-function-generated FD (RBF-FD) has been proven successful in modelling seismic wave propagation based on mesh-free discretisation. Using RBF-FD, we develop a hybrid ABC for piecewise smooth curved boundary in 2D acoustic wave modelling based on straightforward expanding strategies for sampled boundary and corner nodes. The whole irregular computational domain is combined by an objective zone and a transition zone separated by piecewise smooth curved boundary. Nodal distribution in the objective zone is adaptive to the model structure through special alignment and varying density of nodes, while the transition zone are designed for solving one way wave equation more easily and accurately in the presence of piecewise smooth curved boundary. Modelling examples for homogenous and heterogeneous models with differently shaped computational domains demonstrate the effectiveness of our proposed method.

Piecewise chemostat model with control strategy

The chemostat model involving control strategy is either on or off which can be defined by piecewise (or non-smooth) dynamic system. With the aim of controlling the concentration of microorganism within a reasonable range, piecewise chemostat models concerning control strategy with two thresholds are established and investigated. For the chemostat models with a single threshold, all types of equilibria are addressed. Then local bifurcations with respect to boundary node bifurcations are studied by utilizing theoretical and numerical methods. Furthermore, global bifurcations involving touching bifurcation of the sliding cycle, buckling bifurcation of the sliding cycle and sliding crossing bifurcation are discussed. For the chemostat models with two thresholds, No control state and Control state switches are needed to maintain periodic oscillations for microorganism population. Besides, the effects of width of threshold window on the durations or number of Control state and No control state switches are discussed, if the threshold window becomes too large or small, then periodical fluctuation cannot be maintained. Moreover, under certain conditions the microorganism concentration always fluctuates periodically no matter how the threshold window changes. All results indicate that the microorganism concentration can either fluctuate periodically or stabilize at different constants. Therefore, the threshold windows should be chosen carefully according to different aims of control.

CWBound: boundary node detection algorithm for complex non-convex mobile ad hoc networks

Efficient message forwarding in mobile ad hoc network in disaster scenarios is challenging because location information on the boundary and interior nodes is often unavailable. Information related to boundary nodes can be used to design efficient routing protocols as well as to prolong the battery power of devices along the boundary of an ad hoc network. In this article, we developed an algorithm, CWBound, which discovers boundary nodes in a complex non-convex mobile ad hoc (CNCAH) networks. Experiments show that the CWBound algorithm is at least three times faster than other state-of-the-art algorithms, and up to 400 times faster than classical force-directed algorithms. The experiments also confirmed that the CWBound algorithm achieved the highest accuracy (above 97% for 3 out of the 4 types of CNCAH networks) and sensitivity (90%) among the algorithms evaluated.

Target Tracking Based on Virtual Grid in Wireless Sensor Networks

One of the most important and typical application of wireless sensor networks (WSNs) is target tracking. Although target tracking, can provide benefits for large-scale WSNs and organize them into clusters but tracking a moving target in cluster-based WSNs suffers a boundary problem. The main goal of this paper was to introduce an efficient and novel mobility management protocol namely Target Tracking Based on Virtual Grid (TTBVG), which integrates on-demand dynamic clustering into a cluster- based WSN for target tracking. This protocol converts on-demand dynamic clusters to scalable cluster-based WSNs, by using boundary nodes and facilitates sensors’ collaboration around clusters. In this manner, each sensor node has the probability of becoming a cluster head and apperceives the tradeoff between energy consumption and local sensor collaboration in cluster-based sensor networks. The simulation results of this study demonstrated that the efficiency of the proposed protocol in both one-hop and multi-hop cluster-based sensor networks.

An automatic quadrilateral mesh generation algorithm applied to 2-D overland flow simulations

This paper presents an automatic quadrilateral mesh generation algorithm to provide 2-D meshes for simulating overland flow and transport problems in watershed systems. The conformal mapping method is studied deeply and specific treatment strategies are established according to the width of rivers and the area of other water storage zones. A conformity treatment method is proposed to deal with the incompatibility problems during discretizing the complex geometry with a plurality of sub-domains. This method ensures grid conformity through removing certain overlapped nodes and creating new appropriate nodes on common boundaries of the multi-domain mesh. Aiming at the undesired deviation of mesh boundaries from geometric contours, a relative position-percent interpolation method is proposed and a supplementary match method related to dead ends is presented. And, the double effects of projection and smooth for boundary nodes are achieved. An objective function method is proposed to locally optimize the degenerated quadrilaterals located on concave or large-curvature curves. In order to accommodate the need for overland simulations, the 1-D/2-D correspondence on river reaches, junctions with and without storage, ponds, lakes, dead ends and control structures is established. Finally, practical applications are provided to demonstrate the accuracy and reliability of the quadrilateral meshing algorithms proposed in this paper.

A GE/BC imbedded local polynomial collocation method for two dimensional multivariable problems

In this study, a meshless numerical method for 2D problems with 2 variables coupled together in 2 partial differential equations (PDEs) is proposed. This method employs the local polynomial approximation with the weighted-least-squares (WLS) approach. A very distinguishing feature of this method from other collocation methods is the governing equations are satisfied at boundary nodes as well as the boundary conditions. By doing so the strong-form collocation method would be more stable. The 2D elasto-statics analysis is chosen for demonstrating the performance. Three test cases are implemented and the results are compared with exact or analytic solutions. Very good agreements are found.

A study of wall boundary conditions in pseudopotential lattice Boltzmann models

The effect of fluid–solid interactions on the hydrodynamics of non-ideal fluids and wettability of surfaces is investigated. We integrate the interaction forces, simulated by pseudopotentials, into two on-site boundary conditions: standard bounce-back (SBB) and Zou and He (ZH) [12] to determine the distribution functions of the boundary nodes. Three different interaction forces are tested: pseudopotential-based interaction (ψ), modified pseudopotential-based interaction (mψ), and a ZH-based interaction, which is proposed by this study based on the ZH method. Therefore, the schemes are ψ-SBB, mψ-SBB, mψ-ZH, and ZH-ZH. The first criterion is the achievement of macroscopic Poiseuille flow. The second criterion is the achievement of a wide range of contact angles. The main method of simulation is multipseudopotential interaction [30]. It is found that the scheme of ψ-SBB creates a relatively large fluctuation of density across the channel. Whilst, the schemes of mψ-SBB, mψ-ZH, and ZH-ZH generate much less density variation across the channel. Among them, ZH-ZH treatment is superior based on density fluctuation and the error associated with the resolution, relaxation time, and compressibility. We found that all four boundary conditions can form a wide of range of contact angles. The ψ-SBB scheme creates largest density fluctuation inside a drop on wettable surfaces. The schemes of mψ-SBB and mψ-ZH create almost the same density fluctuation which is larger than ZH-ZH. Moreover, mψ interaction generates spurious velocities as high as six times a free drop with SBB and eight times with ZH while spurious velocities in ψ-SBB and ZH-ZH are very close to the free drop. Therefore, ZH-ZH performs best, also, in wettability tests.

Static, dynamic and buckling analyses of 3D FGM plates and shells via an isogeometric-meshfree coupling approach

This paper develops a three-dimensional (3D) isogeometric analysis (IGA) and meshfree coupling approach to investigate the static, dynamic and buckling behaviors for plates and shells of functionally graded material (FGM). The meshfree method and IGA are coupled using the higher-order consistency condition in the physical domain so that the higher-order continuity of basis functions is guaranteed, and the topological complexity of the global volumetric parameterization for IGA to build the 3D geometry can be overcome. By employing IGA elements on the domain boundary and meshfree nodes in the interior domain, the approach preserves the advantages of the exact geometry and flexible discretization in the problem domain. Based on the coupling approach, the analyses for FGM plates and shells are carried out, and the effects of the material volume fraction, the side-to-thickness ratio and the curvature of the cylindrical shell on the deflection, natural frequency, and buckling load are investigated. The coupling approach is verified by comparing with the solutions obtained from other existing theories.

Simulating Fluid and Structure Interaction using Exponential Basis Functions

In this paper a meshless method using exponential basis functions is developed for fluid-structure interaction in liquid tanks undergoing non-linear sloshing. The formulation in the fluid part is based on the use of Navier-Stokes equations, presented in Lagrangian description as Laplacian of the pressure, for inviscid incompressible fluids. The use of exponential basis functions satisfying the Laplace equation leads to a strong form of volume preservation which has a direct effect on the accuracy of the pressure field. In a boundary node style, the bases are used to incrementally solve the fluid part in space and time. The elastic structure is discretized by the finite elements and analyzed by the Newmark method. The direct use of the pressure, as the potential of the acceleration, helps to find the loads acting on the structure in a straight-forward manner. The interaction equations are derived and used in the analysis of a tank with elastic walls. The overall formulation may be implemented simply. To demonstrate the efficiency of the solution, the obtained results are compared with those obtained from a finite elements solution using Lagrangian description. The results show that while the wave height and the oscillations of elastic walls of the two analyses are in good agreement with each other; the use of the proposed meshless analysis not only leads to accurate hydrodynamic pressure but also reduces the computational time to one-eighth of the time needed for the finite elements analysis.

A model order reduction method for the simulation of gear contacts based on Arbitrary Lagrangian Eulerian formulation

Gear contact problems are characterized by a large number of possible contact scenarios while only a few of them are simultaneously active at a given time. When applying the model order reduction method in gear contact problems, the addition of a static shape vector for each possibly-loaded boundary Degree of Freedom (DOF) will enable the contact being accurately described but may be computationally expensive when the number of boundary DOF is large. On the other hand, omission of boundary DOF, though might be computationally efficient, will result in a slow convergence. The objective of this paper is to develop a modeling technique based on Arbitrary Lagrangian Eulerian (ALE) formulation to reduce DOF while providing accurate gear meshing contact simulation. Four techniques are adopted to achieve the critical objective of the paper. First, the low-frequency approximation is attained by ignoring fixed boundary normal modes. Second, under the framework of ALE formulation, only the mesh nodes of four engaging tooth-faces are defined as boundary nodes during the whole process resulting in a great reduction of DOF of the system. Then, the calculation of inertial force and Jacobian matrix are simplified by ignoring the inertial forces resulted from deformation. Finally, a four-step high-efficiency contact algorithm is adopted to reduce the number of contact pairs and accelerate the detection process. The performance of the proposed method is demonstrated with four gear contact problems and correlated with commercial nonlinear finite element software.

Nonlinear Response Characteristics of Undersea Shield Tunnel Subjected to Strong Earthquake Motions

ABSTRACTEnsuring the safety of undersea shield tunnels constructed in soft marine deposits that are subject to strong seismic motion represents a major engineering challenge. An example of one such undersea shield tunnel is the 2.70 km-long subsea highway tunnel crossing under the Gulf of Suai in the Rongjiang River Estuary in Shantou, China. Using the generalized response displacement method, the authors developed a nonlinear seismic response analysis of the segmental lining for the 2.7 km-long Suai tunnel. In the proposed longitudinal seismic response analysis, the engineering geology characteristics and nonlinear dynamic behavior of the Suai seabed soil, the nonuniform mesh layout of the free-field site, the artificial boundary conditions and nonuniform seismic input, simulation model, and the parameters of soil-tunnel interaction systems, are considered in detail. Special emphasis is given to the irregular unloading-reloading rules for the stress-strain hysteresis loop, the seismic input at artificial boundary nodes, and the spatial incoherency of ground motions in the seabed site. The opening width at the ring intersegment under simultaneous actions of longitudinal, transversal, and vertical seismic motions is critical for seismic safety. The proposed methodology was deemed conservative, as demonstrated by a comparison with dynamic transient analysis using the three-dimensional finite element method. The results of this pilot study should be of use in the construction of future long subsea shield tunnels in the high seismic intensity region.

A novel hybrid meshless method for seepage flows in non-homogeneous and anisotropic soils

PurposeThe purpose of this paper is to extend the scaled boundary radial point interpolation method (SBRPIM), as a novel semi-analytical scheme, to the analysis of the steady state confined seepage flows.Design/methodology/approachThis method combines the advantages of the scaled boundary finite element method and the BRPIM. In this method, only boundary nodes are used, no fundamental solution of the problem is required, and as the shape functions constructed based on the RPIM satisfy the Kronecker delta function property, the boundary conditions of problems can be imposed accurately and easily.FindingsThree numerical examples, including seepage flow through homogeneous and non-homogeneous soils, are analyzed in this paper. Comparing the flow net obtained by SBRPIM and other numerical methods confirms the ability of the proposed method in analyzing seepage flows. In addition, in these examples, the accuracy of the SBRPIM in modeling the velocity singularity at a sharp corner is illustrated. SBRPIM accurately models the singularity point in non-homogeneous and anisotropic soil.Originality/valueSBRPIM method is a simple effective tool for analyzing various kinds of engineering problems. It is easy to implement for modeling the velocity singularity at a sharp corner. The proposed method accurately models the singularity point in non-homogeneous and anisotropic soil.

A stabilized moving Kriging interpolation method and its application in boundary node method

Moving Kriging interpolation (MKI) is an important approximation method to construct shape functions in meshless methods. We analyzed the stability of MKI and found that it will become unstable when the nodal spacing decreases. Thus, we developed a stabilized MKI method by using shifted and scaled polynomial basis functions. Then, we applied the stabilized MKI to boundary node method for Laplace's problems and Poisson's problems to study the advantages. For Poisson's problems, the radial integration method is introduced to compute the domain integrals. We also applied the stabilized MKI to element-free Galerkin method to solve elastodynamic problems. Examples are provided to show the accuracy and stability of the stabilized MKI and the boundary node method and element-free Galerkin method based on the stabilized MKI.

Numerical simulation of external flow around cylinder using improved lattice Boltzmann method

In this study, incompressible and viscous external flow around a cylinder is simulated using the lattice Boltzmann method. The surface of cylinder is considered to be a rigid immersed body in the fluid flow. The fluid flow field is discretised by a uniform and fixed Cartesian mesh but there are difficulties in the modelling of curved boundaries. As a result, the cylinder surface is extrapolated by macroscopic properties at boundary nodes. On the other hand, to well treat with boundary condition of the cylinder surface and in the meantime, to save the computational effort, an innovation is applied in this research which solves this problem by introducing a new curved boundary condition to improve computational accuracy in lattice Boltzmann simulations. However, this method can be extended to other physical fields as well as fluid flow. The present results have been compared with the available numerical results which show good agreements.

An explicit algorithm for imbedding solid boundaries in Cartesian grids for the reactive Euler equations

We present a local and point-wise scheme for imposing reflective boundary conditions to stationary internal boundaries for solving the reactive Euler equations on Cartesian grids. The scheme is presented in two and three dimensions and can run efficiently on parallel machines while still maintaining the same advantages over other methods for enforcing internal boundary conditions. Level sets are used to represent internal solid regions along with a new local node sorting algorithm that decouples internal boundary nodes by establishing their connectivity to other internal boundary nodes. This approach allows us to enforce boundary conditions via a direct procedure, removing the need to solve a coupled system of equations numerically. We examine the accuracy and fidelity of our internal boundary algorithm by simulating flows past various solid boundaries in two and three dimensions, showing good agreement between our numerical results and experimental data.

Surveillance of sensitive fenced areas using duty-cycled wireless sensor networks with asymmetrical links

This paper presents a cross-layer communication protocol for Wireless Sensor Network (WSN) enabled surveillance system for sensitive fenced areas, e.g., nuclear/oil site. Initially, the proposed protocol identifies the boundary nodes of the deployed WSN to be used as sentinel nodes, i.e., nodes that are always in active state. The remaining nodes are used as duty-cycled relay nodes during the data communication phase. The boundary nodes identification process and data routing are both performed using an enhanced version of the Greedy Perimeter Stateless Routing (GPSR) protocol, which relies on a Non Unit Disk Graph (N-UDG) and referred to as GPSR over Symmetrical Links (GPSR-SL). Both greedy and perimeter modes of GPSR-SL forward data through symmetrical links only. Moreover, we apply the Mutual Witness (MW) fix to the Gabriel Graph (GG) planarization, to enable a correct perimeter routing on a N-UDG. Simulation results show that the proposed protocol achieves higher packet delivery ratio by up to 3.63%, energy efficiency and satisfactory latency when compared to the same protocol based on the original GPSR.

Singular boundary method based on time‐dependent fundamental solutions for active noise control

Active noise control is an efficient strategy of noise control. A numerical wave shielding model to inhibit wave propagation, which can be considered as an extension of traditional active noise control, is established using the singular boundary method using time‐dependent fundamental solutions in this study. Two empirical formulas to evaluate the origin intensity factors with Dirichlet and Neumann boundary conditions are derived respectively. In comparison with other similar numerical methods, the method can obtain highly accurate results using very few boundary nodes and small CPU time. These meet the major technical requirements of simulation of active noise control. The subsequent numerical experiments show that the proposed model can shield efficiently from the wave propagation for both inner and exterior problems. By applying the newly derived empirical formulas, the CPU time of the singular boundary method is further reduced significantly, which makes the method a competitive new and efficient meshless method. In addition, the singular boundary method makes active noise control in an online manner via time‐dependent fundamental solutions as its basis functions.

Online Determination of External Network Models Using Synchronized Phasor Data

This paper proposes an online measurement-based method for determining multiport Thevenin equivalent circuit parameters of an external power system. The equivalent circuit is estimated using synchronized voltage and current phasors measured at the boundary nodes and it is intended to work continuously leading to real-time equivalent models of the external system. The measurement errors and noise are taken into account by utilizing extra measurements and applying the least-squares method to find the equivalent model parameters. A method to determine the origin of the disturbances is proposed to detect system changes that can be used for the parameter identification process. The performance of the proposed method has been demonstrated by using the IEEE 118 bus system.

NE-IIBEFM for problems with body forces: A seamless integration of the boundary type meshfree method and the NURBS boundary in CAD

A NURBS-enhanced interpolating boundary element-free method (NE-IIBEFM) is proposed by coupling the meshfree method with the non-uniform rational B-spline (NURBS). The NURBS plays an essential role in computer aided design (CAD) whereby it can be used as the bridge between boundary type meshless method and CAD, which is convenient and is widely utilized in engineering. The NURBS basis functions used in CAD packages for geometry construction are applied to describe the boundary in the numerical procedure. Thus, the geometry of the curve can be reproduced exactly at all stages. The boundary integral cells and nodes are defined from the knot vector in NURBS, and both the open and closed curves are considered. The fields are approximated by an improved interpolating moving least square method, in which the obtained shape functions have the property of delta function. Thus, the boundary conditions can be imposed directly. A line integration method without domain discretization is further coupled with the proposed method for the treatment of domain integrals for problems with body forces.

Dynamic analysis of the rope-sheave system of polar crane for nuclear power plant

A systematic method for analyzing the dynamic of the rope-sheave system of polar crane for nuclear power plant is proposed taking physical structure of the system into account based on the virtual power principle in this paper. The dynamical equations of the spatial ropes are established by spline interpolation based on the spatial description parameters, which could be applied to the rope with variable length. For sheaves of different types, the corresponding essential parameters and the virtual power equations are given. Properties and formulations of the variables involved in these equations are studied in detail. In order to improve the solving efficiency, the high-frequency items are filtered out by replacing the instant strain by time- average strain in integral and the degree of freedoms (DOFs) of the spatial ropes are condensed to the boundary nodes of the ropes. Hence, the total virtual power equation in terms of the sheaves’ parameters is obtained. Two numerical examples, including lowering the load and hoisting the load for different types of rope-sheave systems, are given to verify the rationality and feasibility of the method.