Existing Boundary Conditions Research Articles

A boundary condition-damping spring for simulating the acoustoelastic effects of Lamb waves

Physical field simulation is considered an efficient and economical method to study the acoustoelastic effect. Therefore, many researchers thirst for a suitable boundary condition for effectively absorbing incoming waves and reducing echoes while applying pre-stress to the study object, so that the acoustoelastic effects can be more clearly observed by time-domain information of simulation results. However, the existing boundary conditions in physical field simulation software perform helplessly. For this reason, a boundary condi-tion named “damping spring” is proposed in this paper and the corresponding parameter setting scheme is given, effectively solving the above contradiction. Then the feasibility of this boundary condition is verified in 2D and 3D models. In addition, the damping spring boundary condition is applied in this paper to the simulate the acoustoelastic effect of S0-mode Lamb waves in metal plate structures, whose rule shows a good consistency with that of the known literature [5], further verifying the feasibility of the damping spring boundary condition applied to simulate the acoustoelastic effects.

Theory of the momentum source method for synthetic turbulence

The interaction between turbulence and blade leading edges is known to have a significant impact on the aerodynamic and aeroacoustic performance of propellers. In addition to directly simulating turbulence, synthetic turbulence, such as the momentum source method, has been developed as a popular method for studying this interaction process in computational fluid dynamics and computational aeroacoustics. However, it is found that for non-periodic disturbances, although the induced velocity field is divergence-free, spurious noise may be generated in the source region and contaminate simulation results. To address this issue, the present work proposes adding a correction term so that the divergence-free condition is satisfied globally and the unwanted acoustic waves are suppressed, as an extension to our previous work for time-periodic gusts [H. Jiang, Phys. Fluids 35, 096115 (2023)]. The strength of the proposed approach lies in its simplicity, flexibility, and generality. First, it derives explicit source terms, which are straightforward for numerical implementations, to generate unsteady flow fluctuations. Second, the sources can be added inside the computational domain, saving computational costs for turbulence convection and being compatible with most existing boundary conditions. Third, the proposed method can obtain analytical expressions for the needed momentum source of the Navier–Stokes equation subject to any desired isotropic or anisotropic divergence-free turbulence fields. The method has been verified by examples of synthesizing harmonic gusts, Gaussian eddies, and random turbulence. The synthetic velocity results characterized by different spectral components are directly compared to target velocity fields, verifying the proposed approach and showing its capability. Parameters that influence the distribution of added sources are systematically investigated to identify an optimal combination for different scenarios. Finally, the model is employed to evaluate the aerodynamic interaction between an incoming turbulence and a thin airfoil. The obtained results exhibit good correspondence with analytical solutions.

Steady-state simulation of groundwater flow in Khartoum state, Sudan

AbstractThe multi-aquifer system of the Nubian aquifer in central Sudan hydrogeological system was simulated using a three-dimensional steady-state model. The goal of the study is to detect the effect of pumping on the groundwater flow and thus, the aquifer productivity. The conceptual model of the study area was built based on the available geological and hydrogeological data guided by geophysical survey. Processing MODFLOW numerical code was used to calculate the hydraulic head and water balance under the existing boundary conditions. The model accurately simulated the hydraulic head with a determination coefficient of 0.88. The calibrated model indicated that the change in storage is 0.56 m3/day indicating the study area constitutes highly productive zone and is recommended for groundwater developments.

A modified friction-viscous solid boundary of the SPH method for landslide simulation

Bed friction characteristics are important factors controlling landslide movement processes. To address existing boundary condition deficiencies in describing the bed friction characteristics of landslide movements on complex terrain for the SPH method, a modified friction-viscous solid boundary condition is proposed. Within the solid boundary condition, the solid boundary is composed of line segments in 2D conditions and triangular segments in 3D conditions. The solid boundary is treated as a rigid material, and the SPH particle is treated as an elastic particle. The method used to calculate the values and directions of the contact, friction and viscous forces is presented. The proposed solid boundary condition is validated through water and granular material column collapse experiments. The dynamic process of a realistic landslide on complex terrain is simulated to demonstrate the applicability of the proposed solid boundary condition. Compared with the existing solid boundary condition, the proposed solid boundary condition has advantages in embedding friction model and wall function, exerting friction and viscosity force, keeping the stability of contact force, and establishing a complex terrain model.

Avoiding structural redundancies between the vehicle body and the battery housing based on a functional integration approach

In this paper, the approach for a functionally integrated battery housing is presented, to avoid structural redundancies towards the vehicle body. The goal is to reduce the overall structural weight while simultaneously increasing the package space for battery modules. The typically existing boundary conditions for the battery system are taken into account. Especially, the detachability of the battery as a closed unit is in focus, to ensure the leak tightness of this system and to enable replacement. Based on the available space in a research vehicle, such a functionally integrated concept is developed. In particular, the vehicle floor and the vehicle rocker are identified as suitable components for integration. The verification of the concept with regard to the crash performance is carried out on component and on full vehicle level. On both levels, the side pole impact is used as load case and the deformation behavior is investigated.

A fluid–structure interaction model for free-surface flows and flexible structures using smoothed particle hydrodynamics on a GPU

This paper presents the development of a numerical model for violent hydrodynamics of free-surface flows interacting with flexible structures using the meshless smoothed particle hydrodynamics (SPH) method accelerated with a graphics processing unit (GPU). The present work implements a unified SPH framework to solve both the fluid and structural dynamics within the open-source SPH code DualSPHysics. Well-known deficiencies with SPH-based structural modelling (linear inconsistency, tensile instability and rank deficiency) are addressed by adopting a Total Lagrangian formulation with kernel correction and zero-energy mode suppression. The fluid–structure coupling is handled via manipulation of the existing boundary condition within DualSPHysics, which does not require any geometrical knowledge of the interface. This, together with the unified SPH framework, permits straightforward implementation within DualSPHysics and retains its parallel scalability on hardware acceleration platforms, in particular on GPUs. An extensive validation and profiling of the proposed model is carried out for a range of challenging 2-D and 3-D test cases incorporating violent free-surface flows, nonlinear structural dynamics and complex fluid–structure interactions, and its performance is characterised and quantified. The analysis shows good agreement between the proposed model and analytical/benchmark solutions from the literature. Furthermore, the GPU profiling shows speedups on a single GPU of up to 40, compared to an optimised 12-core (24 threads) central processing unit (CPU) version. These findings indicate the proposed model is a viable and efficient approach to simulating violent free-surface fluid–structure interactions.

Novel existence techniques on the generalized \u03c6-Caputo fractional inclusion boundary problem

Our basic purpose is to derive several existence aspects of solutions for a novel class of the fractional inclusion problem in terms of the well-defined generalized φ-Caputo and φ-Riemann–Liouville operators. The existing boundary conditions in such an inclusion problem are endowed with mixed generalized φ-Riemann–Liouville conditions. To reach this goal, we utilize the analytical methods on α-ψ-contractive maps and multifunctions involving approximate endpoint specification to derive the required results. In the final part, we formulate an illustrative simulation example to examine obtained theoretical outcomes by computationally and numerically.

Semi-exact local absorbing boundary condition for seismic wave simulation

AbstractAn absorbing boundary condition is necessary in seismic wave simulation for eliminating the unwanted artificial reflections from model boundaries. Existing boundary condition methods often have a trade-off between numerical accuracy and computational efficiency. We proposed a local absorbing boundary condition for frequency-domain finite-difference modelling. The proposed method benefits from exact local plane-wave solution of the acoustic wave equation along predefined directions that effectively reduces the dispersion in other directions. This method has three features: simplicity, accuracy and efficiency. Numerical simulation demonstrated that the proposed method has higher efficiency than the conventional methods such as the second-order absorbing boundary condition and the perfectly matched layer (PML) method. Meanwhile, the proposed method shared the same low-cost feature as the first-order absorbing boundary condition method.

Investigation of a system of nonlinear fractional order hybrid differential equations under usual boundary conditions for existence of solution

This research work is related to investigate sufficient conditions for existence, uniquely of solution to a coupled system of nonlinear fractional order hybrid differential equations (NFOHDEs). With the help of Burton's fixed point theorem, we develop the required conditions for existence of at least one solution to the considered problem of NFOHDEs.

Research Note: A workaround for the corner problem in numerically exact non‐reflecting boundary conditions

ABSTRACTSimulations of wave propagation in the Earth usually require truncation of a larger domain to the region of interest to keep computational cost acceptable. This introduces artificial boundaries that should not generate reflected waves. Most existing boundary conditions are not able to completely suppress all the reflected energy, but suffice in practice except when modelling subtle events such as interbed multiples. Exact boundary conditions promise better performance but are usually formulated in terms of the governing wave equation and, after discretization, still may produce unwanted artefacts. Numerically exact non‐reflecting boundary conditions are instead formulated in terms of the discretized wave equation. They have the property that the numerical solution computed on a given domain is the same as one on a domain enlarged to the extent that waves reflected from the boundary do not have the time to reach the original truncated domain. With a second‐ or higher‐order finite‐difference scheme for the one‐dimensional wave equation, these boundary conditions follow from a recurrence relation. In its generalization to two or three dimensions, a recurrence relation was only found for a single non‐reflecting boundary on one side of the domain or two of them at opposing ends. The other boundaries should then be zero Dirichlet or Neumann. If two non‐reflecting boundaries meet at a corner, translation invariance is lost and a simple recurrence relation could not be found.Here, a workaround is presented that restores translation invariance by imposing classic, approximately non‐reflecting boundary conditions on the other sides and numerically exact ones on the two opposing sides that otherwise would create the strongest reflected waves with the classic condition. The exact ones can also be applied independently. As a proof of principle, the method is applied to the two‐dimensional acoustic wave equation, discretized on a rectangular domain with a second‐order finite‐difference scheme and first‐order Enquist–Majda boundary conditions as approximate ones. The method is computationally costly but has the advantage that it can be reused on a sequence of problems as long as the time step and the sound speed values next to the boundary are kept fixed.

Enhanced method for pulse skin effect calculation of cylindrical conductors

PurposeThis paper aims to present a new approach to the numerical solution of skin effect integral equations in cylindrical conductors. An approximate, but very simple and accurate method for calculating the current density distribution, skin-effect resistance and inductance, in pulse regime of cylindrical conductor, having a circular or rectangular cross-section, is considered. The differential evolution method is applied for minimization of error functional. Because of its application in the practice, the lightning impulse is observed. Direct and inverse fast Fourier transform is applied.Design/methodology/approachThis method contributes to increasing of correctness and much faster convergence. As the electromagnetic field components depend on the current density derivation, the proposed method gives a very accurate solution not only for current density distribution and resistance but also for field components and for internal inductance coefficients. Distribution of current and electromagnetic field in bus-bars can be successfully determined if the proximity effect is included together with the skin effect in calculations.FindingsThe study shows the strong influence of direct lightning strikes on the distribution of electrical current in cables used in lightning protection systems. The current impulse causes an increase in the current density at all points of the cross-section of the conductor, and in particular the skin effect on the external periphery. Based on the data calculated by using the proposed method, it is possible to calculate the minimum dimensions of the conductors to prevent system failures.Research limitations/implicationsThere are a number of approximations of lightning strike impulse in the literature. This is a limiting factor that affects the reliability and agreement between measured data with calculated values.Originality/valueIn contrast with other methods, the current density function is approximated by finite functional series, which automatically satisfy wave equation and existing boundary conditions. It is necessary to minimize the functional. This approach leads to a very accurate solution, even in the case when only two terms in current approximation are adopted.

Triggering of Buneman instability and existence of multiple double layers in laboratory plasma

We report experimentally observed triggering criteria for Buneman instability and boundary conditions for existence of multiple double layers (MADL) in glow discharge plasma. The MADLs are generated by accelerating plasma electrons towards a positively biased electrode submerged in it. The boundary conditions for the formation and existence of MADL are obtained from the experiment in terms of electron drift velocity (νd) and electron thermal velocity (νte). The MADL is found to exist within the range 3νte≥νd≥1.3νte. For the condition νd≥1.3νte, rise of an instability and simultaneous formation of MADL is observed in the experiment. The analysis of fluctuations in floating potential showed that the instability has all the characteristics of Buneman instability.

Behavior of structural tunnel elements exposed to fire and mechanical loading

PurposeIncidents like the fire in the Channel Tunnel, where severe concrete spalling was determined, have led to requirements in limiting the spalling depth and involved zone to local and compatible magnitudes. Because the prevention of critical concrete spalling was also significant for the validity of the load-carrying capacity calculation for an existing railway tunnel, this paper aimed to investigate the spalling behavior of two contemplable concrete mixtures. The large-scale tests should show the load-carrying capacity over the whole duration of the fire exposure respecting all thermal and mechanical loads considered in the calculations.Design/methodology/approachIn this paper, the fire behavior of two concrete mixtures for an existing railway tunnel are investigated. Small-scale tests prior to the main tests were conducted to identify an appropriate concrete mixture for the large-scale tests. During the large-scale tests, a tunnel segment is loaded with horizontal and vertical loads derived from a calculation taking into account the existing boundary conditions. Resulting restraint forces were calculated using the soil stiffness and tunnel fire design curve as fire scenario and applied via hydraulic jacks. To avoid additional restraint forces during the experiment, thermal strains due to fire exposure were allowed.FindingsThe results of the small-scale tests did not allow for a clear statement whether one concrete mixture would perform better regarding the spalling behavior. The two large-scale tests showed different results regarding the spalling behavior. Over the whole duration of fire exposure, the first test specimen remains nearly undamaged. During the test of the second specimen, spalling started about 3 min after burner activation. Because of the results, a suggestion for the concrete mixture of the first test was made, and this mixture was then used for the redevelopment of the existing railway tunnel.Originality/valueThe test setup was capable of incorporating all relevant boundary conditions for the analysis of an existing railway tunnel as part of an important north – south connection. The results have shown that a fire-proof construction is possible by adding polypropylene fibers to the concrete mixture. Additionally, it was possible to avoid the mounting of expensive and time-consuming fire protection measures like the installation of thermal insulation boards.

Scaling Hydrodynamic Boundary Conditions of Microstructured Surfaces in the Thin Channel Limit

Despite its importance in many applications and processes, a complete and unified view on how nano- and microscale asperities influence hydrodynamic interactions has yet to be reached. In particular, the effects of surface structure can be expected to become more dominant when the length scale of the asperities or textures becomes comparable to that of the fluid flow. Here we analyze the hydrodynamic drainage of a viscous silicone oil squeezed between a smooth plane and a surface decorated with hexagonal arrays of lyophilic microsized cylindrical posts. For all micropost arrays studied, the periodicity of the structures was much larger than the separation range of our measurements. In this thin channel geometry, we find the hydrodynamic drainage and separation forces for the micropost arrays cannot be fully described by existing boundary condition models for interfacial slip or a no-slip shifted plane. Instead, our results show that the influence of the microposts on the hydrodynamic drag exhibits three distinct regimes as a function of separation. For large separations, a no slip boundary condition (Reynolds theory) is observed for all surfaces until a critical (intermediate) separation, below which the position of the no-slip plane scales with surface separation until reaching a maximum, just before contact. Below this separation, a sharp decrease in the no-slip plane position then suggests that a boundary condition of a smooth surface is recovered at contact.

A modulation equations approach for numerically solving the moving soliton and radiation solutions of NLS

Based on our previous work for solving the nonlinear Schrödinger equation with multichannel dynamics that is given by a localized standing wave and radiation, in this work we deal with the multichannel solution which consists of a moving soliton and radiation. We apply the modulation theory to give a system of ODEs coupled to the radiation term for describing the solution, which is valid for all times. The modulation equations are solved accurately by the proposed numerical method. The soliton and radiation are captured separately in the computation, and they are solved on the translated domain that is moving with them. Thus for a fixed finite physical domain in the lab frame, the multichannel solution can pass through the boundary naturally, which cannot be done by imposing any existing boundary conditions. We comment on the differences of this method from the collective coordinates.

Performance of the Double Absorbing Boundary Method when Applied to the 3D Acoustic Wave Equation

SUMMARY The double absorbing boundary (DAB) is a new highorder absorbing boundary condition for the scalar acoustic wave equation. It suppresses scattered waves at the edge of a boundary layer in computational domain boundary by using destructive interference analogous to a noise-cancelling headphone. This method has advantages in that it addresses some of the shortfalls in existing boundary conditions, such as the need for tuning in Perfectly Matched Layers or complex formulations at corners such as in high-order absorbing boundary conditions. We extend the original formulation of the DAB to three dimensions and higher-order stencils. Through numerical simulation we test the performance of the DAB by comparison with a reflecting boundary. We find that the DABC is a broadband attenuator with a power attenuation of 20-30dB using only six boundary cells. Increasing the order of the method improves accuracy for wavelengths less than 10 cells, whereas increasing the layer width does not improve accuracy. The method shows promise as a robust and computationally efficient boundary condition for seismic applications.

Lattice Boltzmann simulations of pressure-driven flows in microchannels using Navier–Maxwell slip boundary conditions

We present lattice Boltzmann simulations of rarefied flows driven by pressure drops along two-dimensional microchannels. Rarefied effects lead to non-zero cross-channel velocities, and nonlinear variations in the pressure along the channel. Both effects are absent in flows driven by uniform body forces. We obtain second-order accuracy for the two components of velocity and the pressure relative to asymptotic solutions of the compressible Navier–Stokes equations with slip boundary conditions. Since the common lattice Boltzmann formulations cannot capture Knudsen boundary layers, we replace the usual discrete analogs of the specular and diffuse reflection conditions from continuous kinetic theory with a moment-based implementation of the first-order Navier–Maxwell slip boundary conditions that relate the tangential velocity to the strain rate at the boundary. We use these conditions to solve for the unknown distribution functions that propagate into the domain across the boundary. We achieve second-order accuracy by reformulating these conditions for the second set of distribution functions that arise in the derivation of the lattice Boltzmann method by an integration along characteristics. Our moment formalism is also valuable for analysing the existing boundary conditions. It reveals the origin of numerical slip in the bounce-back and other common boundary conditions that impose conditions on the higher moments, not on the local tangential velocity itself.

On pressure and corner boundary conditions with two lattice Boltzmann construction approaches

A pressure (density) and a corner no-slip boundary condition formulation are introduced for the two-dimensional lattice Boltzmann method and numerically tested for the Hagen–Poiseuille flow case in this work. Both formulations are derived independently of the equilibrium distribution function model and no bounce-back rule is needed. The corners are free of interpolations and are implemented with collisions. The Hermite-based and the “entropy”-based lattice Boltzmann constructions are reviewed, described in some details and compared. The best two models from each approach are chosen. An indirect substitution of the boundary values in the equilibrium distribution function is further expanded to its “entropic” counterpart. For the straight walls, two existing boundary conditions with first and second order of accuracy are selected. The numerical results demonstrate that the presented boundary conditions are capable to preserve up to the second order of accuracy, depending on the straight walls. Based on the theoretical and numerical results, the so called Hermite construction is the recommended approach for isothermal incompressible flows.

Cracks propagation and interaction in an orthotropic elastic material: Analytical and numerical methods

Abstract An elastic orthotropic material containing a crack in Mode I is considered to formulate a new analytical model. The boundary conditions for the crack existence in the material lead to the solution of the homogeneous Riemann–Hilbert problems. The mathematical model was elaborated for a single and two collinear cracks of different lengths and distance for Mode I in order to investigate cracks interaction problem. Using the theory of Cauchy’s integral and the numerical analysis, the fields in the vicinity of the crack tips were determined. Finite Element Method was applied to compare the mathematical analytical solution and to determine the fields in the vicinity of the crack tips. The critical values of applied stress which caused cracks propagation were evaluated. The interaction of cracks in an orthotropic aramid-epoxy material was studied in details. Comparison of both approaches to crack propagation leads to the conclusion that the new analytical model is correct and can be applied to more complex cracks geometries, including inclined cracks.

Heat, Air, and Moisture Control in Slab-on-ground Structures

The objective of this research is to determine the heat, air, and moisture conditions of slab-on-ground of a heated building. Measurements show that the coarse-grained fill or drainage layers beneath heated slab-on-ground structures are warm and moist throughout the year. Moisture migration: gravitational water, ground water table, capillary action and diffusion, keep these layer moist throughout the year. The water vapor content of the warm and moist fill layer is usually higher than the content of the indoor air. Thus, the diffusion flow is directed into the indoor air, despite the existing heat flow into the opposite direction, and the ground is a moisture source for the structures above. Therefore, thermal and moisture conditions of the fill layers have the major effect on the overall moisture behavior of ground slabs: on the drying times of the fresh in situ cast concrete slab, and on the thermal and moisture behavior of the structure in normal long-term conditions. These conditions are also favorable for microbe growth, which is very common in fill layers. Fungal or bacterial growth was detected in 98% of the test specimens taken beneath the ground slabs of heated buildings. These conditions: warm fill layers, high moisture level (RH near 100%) and microbe growth, are the normal conditions for the well functioning slab-on-ground structure. They are not a sign of moisture damage, but the existing boundary conditions for the design of ground slabs. Therefore, it is important to prevent air infiltration between the ground and the indoor air, as effective as possible. The adequate sealing of the joints and lead-ins of the floor assure that the impurities do not penetrate the indoor air.