Boundary Treatment Research Articles

Phase-field-based lattice Boltzmann model for liquid-gas-solid flow.

Based on phase-field theory, we develop a lattice Boltzmann (LB) model for liquid-gas-solid flow from multiphase and particle dynamics algorithms. A modified bounce-back method is developed for the velocity-based LB approach. A curved boundary treatment with second-order accuracy based on velocity interpolation is developed. We propose a predictor-corrector scheme algorithm for specifying the three-phase contact angle on curved boundaries within the framework of structured Cartesian grids. In order to make the algorithm more stable, we combine the implicit particle velocity update scheme and the Galilean invariant momentum exchange method. The proposed method is validated through several single- and multicomponent fluid test cases. It was found the surface tension force associated with the interface acting on the solid structures can be captured. We simulate the sinking of a circular cylinder due to gravity, the numerical results agree well with the experimental data. Finally, we apply the method to the self-assembly process of multiple floating cylinders on water surface.

A Lagrangian approach for computational acoustics with particle-based method

Although Eulerian approaches are standard in computational acoustics, they are less effective for problems with moving boundaries and multiphase systems like bubble acoustics. In this paper, a Lagrangian approach to model sound propagation in moving fluid is presented and implemented numerically with particle-based methods. Fluid dynamic equations is divided into a set of hydrodynamic equations for the motion of fluid particles and perturbation equations for the acoustic quantities corresponding to each fluid particle. Then, the smoothed particle hydrodynamics (SPH) method and the corrective smoothed particle (CSP) method are introduced to solve the perturbation equations in Lagrangian form. A hybrid meshfree and finite-difference time-domain boundary treatment technique is utilized to represent acoustic boundaries. Finally, applications to modeling sound propagation in steady or unsteady fluids in motion are outlined, treating a number of different cases in one and two space dimensions. The Lagrangian approach shows good agreement with exact solutions. The comparison indicates that the CSP method exhibits accuracy convergence in cases with different background flow. Different acoustic boundary conditions are validated as being effective for benchmark problems in computational acoustics.

Improved treatment of wall boundary conditions for a particle method with consistent spatial discretization

In recent years, consistent spatial discretization schemes for meshfree particle methods to numerically simulate incompressible flow have been studied by many researchers. This study is focused on the treatment of solid wall boundary conditions for one of those schemes, namely the least squares MPS (LSMPS) scheme, and proposes a new technique to deal with no-slip and free-slip wall boundary conditions. With the proposed treatment, wall geometries are expressed by surface meshes, i.e. polygons in 3D and line segments in 2D. Thus, complicated geometries can be handled easily. Based on a Taylor series expansion, wall boundary conditions are incorporated into the differential operators acting on fluid particles located in the vicinity of a wall, through a least squares approach. As a consequence, Neumann boundary conditions can be treated quite efficiently. To verify consistency of the proposed discretization scheme, a convergence study was carried out. As numerical examples, Couette flow, plane Poiseuille flow, gravity-driven flow in a 3D square duct, a rigid rotation problem, Taylor–Green vortices and lid-driven cavity flow have been calculated using the proposed boundary treatment, with both no-slip and free-slip conditions applied. As a result, the present method agreed well with the reference solutions, which verified its computational accuracy.

Numerical simulation of column charge explosive in rock masses with particle flow code

The detonation of a column charge and the damage process in a rock mass are simulated in this study by the particle flow code method. The expansion loading method and the dynamic boundary treatment method are established according to the discrete element mechanism. Mechanical parameters are calibrated on the basis of the Starfield superposition principle and the dynamic compensation method. Dynamic stiffness and microscopic parameters are used for numerical simulations. Numerical test results are consistent with lab experimental test results. The velocity attenuation law is compared with that of theoretical results, and the blasting crater action index is compared with that of field test results, to verify the rationality of the numerical explosion model of the column charge. The mechanism of the rock breaking process under column charge explosion is analyzed. Stress wave propagation, detonation wave propagation, and crack extension are investigated. The stress wave gradient law is obtained, and the effects of blasting rock breaking, crack extension, and explosion effect outside the blasting crater area are determined with different initiation modes. The research method can explain the blasting stress wave propagation law and describe the dynamical failure process in rock masses. This study can provide a reliable numerical analysis method for follow-up blasting research and offer practical guidance on engineering blasting.

Stability analysis of high-order finite-difference discretizations of the linearized forward-speed seakeeping problem

A high-order finite-difference method solution of the linearized, potential flow, seakeeping problem for a ship at steady forward speed was recently presented by Amini-Afshar et al. [1,2]. In this paper, we provide a detailed matrix-based eigenvalue stability analysis of this model, highlighting the sources of instability and the effects of possible remedies. In particular, we illustrate how both boundary treatment and grid stretching are important factors which are not typically captured by a von Neumann-type analysis. The new analysis shows that when grid stretching is used together with centered finite difference schemes, the method is generally unstable. The source of the instability can in some cases be traced to an effective downwinding of the convective terms. Stable solutions can be obtained either by introducing upwind-biased schemes for computing the convective derivatives on the free-surface, or by application of a mild filter at each time-step. A second source of instability is associated with the treatment of the convective derivatives of the free-surface elevation at points close to the domain boundaries. Here it is necessary to consider whether the surrounding fluid points lie in an upwind or a downwind direction. For upwinded points, ordinary one-sided differencing can be used, but for downwinded points we instead impose a Neumann-type boundary condition derived from the body and free-surface boundary conditions. As an example application to complement those already given in [1,2], the method is applied to solve the steady wave resistance problem and comparison is made to reference solutions for a two-dimensional floating cylinder and a submerged sphere. Estimates of the wave resistance of the Wigley hull are also compared with experimental measurements.

A Meshless WCSPH Boundary Treatment for Open-Channel Flow over Small-Scale Rough Bed

A weakly compressible smoothed particle hydrodynamics (WCSPH) method was developed to model open-channel flow over rough bed. An improved boundary treatment is proposed to quantitatively characterize bed roughness based on the ghost boundary particles (GBPs). In this model, the velocities of GBPs are explicitly calculated by using evolutionary polynomial regression with a multiobjective genetic algorithm. The simulation results show that the proposed boundary treatment can well reflect the influence of wall roughness on the vertical flow structure. A fully developed open channel is established, and its flume length, processing time, and turbulent model are discussed. The mixed-length-based subparticle scale (SPS) turbulence model is adopted to simulate uniform flow in open channel, and this model is compared with the Smagorinsky-based one. For the modified WCSPH model, the results show that the calculated vertical velocity and turbulent shear stress distribution are in good agreement with experimental data and fit better than the calculations obtained from the traditional Smagorinsky-based model.

A comparative study of immersed boundary method and interpolated bounce-back scheme for no-slip boundary treatment in the lattice Boltzmann method: Part II, turbulent flows

In the first part of this study [1], we compared the performances of two categories of no-slip boundary treatments, i.e., the interpolated bounce-back schemes and the immersed boundary methods in a series of laminar flow simulations within the lattice Boltzmann method. In this second part, these boundary treatments are further compared in the simulations of turbulent flows with complex geometry to provide a next-level assessment of these schemes. Two non-trivial turbulent flow problems, a fully developed turbulent pipe flow at a low Reynolds number, and a decaying homogeneous isotropic turbulent flow laden with a large number of resolved spherical particles are considered. The major problem of the immersed boundary method revealed by the present study is its incapability in computing the local velocity gradients inside the diffused interface, which can result in significantly underestimated dissipation rate and viscous diffusion locally near the particle surfaces. Otherwise, both categories of the no-slip boundary treatments are able to provide accurate results for most of turbulent statistics in both the carrier and dispersed phases, provided that sufficient grid resolutions are used. The criteria of sufficient grid resolutions for each examined flow are also addressed in this document.

Lattice Boltzmann study on drag reduction of a bluff body by slip boundary

Slip velocity at boundary will emerge when gas film or superhydrophobic coatings are applied to the surface. The no-slip boundary conditions are no longer efficient. In this work, an improved boundary treatment is proposed to obtain slip velocity. Numerical results of the Couette flow have verified the accuracy and reliability of the improved boundary condition. Taking into account the effect of boundary slip, the present research predicts the resistance of a bluff body under low Reynolds numbers using the lattice Boltzmann method. Results show that reasonable slip distribution may be favourable to the drag reduction effect.

The Inviscid Three Dimensional Quasi-Geostrophic System on Bounded Domains

We present a formal derivation of the inviscid three dimensional quasi-geostrophic system (QG) from primitive equations on a bounded, cylindrical domain. A key point in the derivation is the treatment of the lateral boundary and the resulting boundary conditions it imposes on solutions. To our knowledge, these boundary conditions are new and differentiate our model from closely related models which have been the object of recent study. These boundary conditions are natural for a variational problem in a particular Hilbert space. We construct solutions and prove an elliptic regularity theorem corresponding to the variational problem, allowing us to show the existence of global weak solutions to QG.

Investigations of the Hydraulic Characteristics of Stilling Basin with Baffle-Blocks Using an Integrated SPH Method

The stilling basin has been one of the most powerful hydraulic structures for the dissipation of the flow energy. Meshfree and particle methods have special advantages in modeling incompressible flows with free surfaces. In this paper, an integrated smoothed particle hydrodynamics (SPH) method is developed to model energy dissipation process of stilling basins. The integrated SPH includes the kernel gradient correction (KGC) technique, the dynamic solid boundary treatment, [Formula: see text]-SPH model and density reinitialization. We first conducted the simulations of dam-breaking and hydraulic jump to validate the accuracy of the present method. The present simulation results agree well with the experimental observations and numerical results from other sources. Then the discharge process of stilling basin with baffle-blocks is simulated with the integrated SPH. It is demonstrated that the detailed discharge process can be well captured by this method. The energy dissipation effect of stilling basin could be significantly improved by the baffle-blocks. The structure and position of the baffle-block directly affect the energy dissipation effect, while the height of the baffle-block has big influence on the drainage capacity.

Natural convection from heated fin shapes in a nanofluid-filled porous cavity using incompressible smoothed particle hydrodynamics

Purpose This study aims to focus on the numerical simulation of natural convection from heated novel fin shapes in a cavity filled with nanofluid and saturated with a partial layer of porous medium using improved incompressible smoothed particle hydrodynamics (ISPH) method. Design/methodology/approach The dimensionless of Lagrangian description for the governing equations were numerically solved using improved ISPH method. The current ISPH method was improved in term of wall boundary treatment by using renormalization kernel function. The effects of different novel heated (Tree, T, H, V, and Z) fin shapes, Rayleigh number Ra(103 – 106 ), porous height Hp (0.2-0.6), Darcy parameter Da(10−5 − 10−1 ) and solid volume fraction ϕ(0.0-0.05) on the heat transfer of nanofluid have been investigated. Findings The results showed that the variation on the heated novel fin shapes gives a suitable choice for enhancement heat transfer inside multi-layer porous cavity. Among all fin shapes, the H-fin shape causes the maximum stream function and Z-fin shape causes the highest value of average Nusselt number. The concentrations of the fluid flows in the nanofluid region depend on the Rayleigh and Darcy parameters. In addition, the penetrations of the fluid flows through porous layers are affected by porous heights and Darcy parameter. Originality/value Natural convection from novel heated fins in a cavity filled with nanofluid and saturated with a partial layer of porous medium have been investigated numerically using improved ISPH method.

Parallelization, initialization, and boundary treatments for the diamond scheme

We study a class of general purpose linear multisymplectic integrators for Hamiltonian wave equations based on a diamond-shaped mesh. On each diamond, the PDE is discretized by a symplectic Runge–Kutta method. The scheme advances in time by filling in each diamond locally. We demonstrate that this leads to greater efficiency and parallelization and easier treatment of boundary conditions compared with methods based on rectangular meshes. We develop a variety of initial and boundary value treatments and present numerical evidence of their performance. In all cases, the observed order of convergence is equal to or greater than the number of stages of the underlying Runge–Kutta method.

A conservative and consistent Lagrangian gradient smoothing method for earthquake-induced landslide simulation

Numerical study of earthquake-induced landslides plays an important role in the disaster prevention and post-earthquake managements. Thanks to its mesh-free feature, the SPH (Smoothed Particle Hydrodynamics) method has significant advantages over the traditional grid-based methods in dealing with extremely large deformation problems such as high-speed fluid-like landslides. However, SPH is unstable when the material is in tension, which is widely known as the ‘tensile instability’ problem in SPH. Although the instability issue can be removed to certain stand by particular ad-hoc techniques, the root cause of the problem is not addressed. In addition, such ad-hoc techniques require additional user-defined parameters, which is difficult to make universally applicable. In this study, a conservative and consistent Lagrangian Gradient Smoothing Method (L-GSM) is proposed for fluid-like landslide simulations based on the recently developed meshfree L-GSM. In the present L-GSM, the strong-form of governing equations is discretized using the GSM gradient operator in a conservative and consistent manner. Moreover, a simple and accurate boundary treatment for free surface and solid boundary is newly proposed for L-GSM to handle the complicated free surface and solid boundary existed in the landslide problems. Finally, the proposed conservative and consistent L-GSM framework is validated by a soil column collapse benchmark and three real landslide problems. Results show that our L-GSM can give an accurate and reliable solution to the fluid-like landslide problem with a high efficiency. The treatments for free surface and solid boundary are also proven very effective in producing desired boundary conditions. Both cohesive soil column collapse example and Wangjiayan landslide example demonstrate that L-GSM is indeed free from the tensile instability problem.

An improved predictive-corrective incompressible smoothed particle hydrodynamics method for fluid flow modelling

Predictive-corrective incompressible smoothed particle hydrodynamics (PCISPH) is an efficient SPH variation originally developed for computer graphics. Its application in modeling physics-focused fluid flows has not yet been reported. In this work, an improved PCISPH method is presented for physics-focused fluid flow modeling. Different from traditional weakly-compressible SPH (WCSPH) and incompressible SPH (ISPH), PCISPH satisfies the incompressibility requirement at the particle level without a predefined equation of state. The pressure is obtained using an iterative predictive-corrective scheme at each individual particle. The presented PCISPH allows much larger time steps compared with WCSPH. It also avoids the time-consuming solution of Pressure Poisson Equation (PPE) in ISPH. Consequently, the PCISPH has high computational efficiency even with millions of computational particles. To ensure physically correct modeling of fluid flows, we employ several techniques to enhance the accuracy and stability of the PCISPH: (1) the continuity equation is used to predict density, replacing the mass summation approach used in the original PCISPH, (2) numerical diffusion and pressure smoothing are introduced to improve the pressure computation, (3) a generalized boundary treatment approach which can handle arbitrarily complex geometries is employed, (4) an adaptive time-stepping algorithm is used, allowing efficient simulation as well as ensuring stability. The performance of the improved PCISPH is systematically investigated using three standard SPH validation cases. Comparisons between the improved PCISPH and the state-of-the-art δ — SPH are presented. It is found that the improved PCISPH gives numerical results as accurate as δ — SPH, except for having moderate temporal pressure oscillations. However, the numerical results show that the improved PCISPH is approximately five times faster than δ — SPH. The improved PCISPH method shows to be a promising tool for large-scale three-dimensional fluid flow modeling.

A comparative study of immersed boundary method and interpolated bounce-back scheme for no-slip boundary treatment in the lattice Boltzmann method: Part I, laminar flows

The interpolated bounce-back schemes and the immersed boundary method are the two most popular algorithms in treating a no-slip boundary on curved surfaces in the lattice Boltzmann method. While those algorithms are frequently implemented in the numerical simulations involving complex geometries, such as particle-laden flows, their performances are seldom compared systematically over the same local quantities within the same context. In this paper, we present a systematic comparative investigation on some frequently used and most state-of-the-art interpolated bounce-back schemes and immersed boundary methods, based on both theoretical analyses and numerical simulations of four selected 2D and 3D laminar flow problems. Our analyses show that immersed boundary methods (IBM) typically yield a first-order accuracy when the regularized delta-function is employed to interpolate velocity from the Eulerian to Lagrangian mesh, and the resulting boundary force back to the Eulerian mesh. This first order in accuracy for IBM is observed for both the local velocity and hydrodynamic force/torque, apparently different from the second-order accuracy sometime claimed in the literature. Another problem of immersed boundary methods is that the local stress within the diffused fluid-solid interface tends to be significantly underestimated. On the other hand, the interpolated bounce-back generally possesses a second-order accuracy for velocity, hydrodynamic force/torque, and local stress field. The main disadvantage of the interpolated bounce-back schemes is its higher level of fluctuations in the calculated hydrodynamic force/torque when a solid object moves across the grid lines. General guidelines are also provided for the necessary grid resolutions in the two approaches in order to accurately simulate flows over a solid particle.

GPU accelerated lattice Boltzmann method in neutron kinetics problems II: Neutron transport calculation

The simulation of neutron transport equation (NTE) has become one of the main trends of nuclear reactor engineering and design owing to its high accuracy, wherein one of its limitations is the low computational speed. To improve this condition, this paper provides a GPU accelerated neutron transport lattice Boltzmann method (NTLBM) for solving neutron transport problem. The simplified finite Boltzmann scheme and the GPU CUDA technique are combined to achieve the spatial parallel calculation and the space-angle full parallel calculation. Due to the ease of implementation and high parallelism, the GPU accelerated NTLBM (GPU-NTLBM) can be very easily and efficiently to realize. Besides, by using the multi-GPU acceleration, the large-scale NTLBM engineering calculation can be efficiently speeded up, and the properties of NTLBM makes the internal boundary treatments convenient. In considering the properties of the NTE, the space-angle full parallel acceleration is applied to further speed up the GPU-NTLBM for the first time, in which all the spatial and the angular dimensions are calculated in parallel. Simulation results show that the NTLBM can be applied to solve the multi-group neutron transport problems accurately and the GPU acceleration can be applied to effectively speed up the NTLBM calculation. The space-angle full parallel acceleration can further improve the GPU-NTLBM acceleration. This paper could provide some parallel perspectives for solving the large-scale neutron transport engineering calculation.

Complete mechanical regularization applied to digital image and volume correlation

This paper presents a new regularization scheme for Digital Image Correlation (DIC) and Digital Volume Correlation (DVC) techniques based on the equilibrium gap method with reference to a linear elastic behavior. This scheme constitutes a unique framework for performing the so-called mechanical regularization for any problem dimension. “Complete regularization” refers to the fact that a specific treatment of boundaries (surfaces) is introduced here on the same footing as the bulk, independently of the complexity of their shape. The proposed treatment distinguishes the roles that different boundaries (Neumann or Dirichlet) play in mechanical tests. Numerical cases on synthetic data and a real experimental test validate the robustness and accuracy of the method. The analyzed experiment shows that only the use of (complete) regularization ensures convergence. Even in the cases where such regularization is not employed but convergence is achieved, it is at much higher cost. These results reveal the benefit of regularization on the convergence rate of DVC.

Local uniform stencil (LUST) boundary condition for arbitrary 3-D boundaries in parallel smoothed particle hydrodynamics (SPH) models

This paper presents the development of a new boundary treatment for free-surface hydrodynamics using the smoothed particle hydrodynamics (SPH) method accelerated with a graphics processing unit (GPU). The new solid boundary formulation uses a local uniform stencil (LUST) of fictitious particles that surround and move with each fluid particle and are only activated when they are located inside a boundary. This addresses the issues currently affecting boundary conditions in SPH, namely the accuracy, robustness and applicability while being amenable to easy parallelization such as on a GPU. In 3-D, the methodology uses triangles to represent the geometry with a ray tracing procedure to identify when the LUST particles are activated. A new correction is proposed to the popular density diffusion term treatment to correct for pressure errors at the boundary. The methodology is applicable to complex arbitrary geometries without the need of special treatments for corners and curvature is presented. The paper presents the results from 2-D and 3-D Poiseuille flows showing convergence rates typical for weakly compressible SPH. Still water in a complex 3-D geometry with a pyramid demonstrates the robustness of the technique with excellent agreement for the pressure distributions. The method is finally applied to the SPHERIC benchmark of a dry-bed dam-break impacting an obstacle showing satisfactory agreement and convergence for a violent flow.

Working at the boundary: Making space for innovation in a NASA megaproject

This study shows how occupational, organizational and institutional boundaries can be reworked to enable innovation. Based on an historical case study of NASA's Spitzer Space Telescope, which spanned three decades and two dozen organizations, I show how megaproject members made boundaries a target of strategic action. Megaprojects, in particular, require us to think about boundaries at multiple levels as they commonly draw on expertise and resources from different disciplines, organizations, and institutional domains. This case reveals several mechanisms by which boundaries can be modified to coordinate diverse innovation partners, from reconfiguring the ways members relate to one another (splicing, fitting and channeling) to reshaping the environment they work in (softening, fusing and corralling). Overall, this study contributes to our understanding of how actors make room for new ideas and cause institutional change as part of innovation processes. By treating boundaries as malleable and multiplex, I extend organizational theory, which tends to view boundaries as given and things to be spanned. I extend the STS literature that takes boundaries as fluid, identifying several mechanisms of making and unmaking them. A more dynamic treatment of boundaries is called for in both innovation research and practice, and this study opens a path for research that looks not only at boundary objects but also boundary actions, and moves from boundary organizations to boundary organizing.

Lattice Boltzmann simulation of particle-laden flows using an improved curved boundary condition

In the application of the lattice Boltzmann method (LBM) for the simulation of the interface-resolved particulate flows, the bounce-back (BB) type rules have been widely adopted to handle the complex boundaries of moving particle. However, the original method cannot preserve the integrity of the particle shape, resulting in a low-resolution for the flow description near the solid boundary. Even though the subsequent modified BB scheme, i.e. the curved boundary condition (CBC), improves the overall accuracy, it generally loses the local-computation property of the simple BB. Therefore, a CBC is proposed in this paper, which maintains the two advantages of the second-order accuracy and local computation in the boundary treatment simultaneously. In the present scheme, information of only a single fluid point is needed. Furthermore, the relative distance between the fluid point and the boundary surface is involved, contributing to the second-order accuracy that is validated in the Poiseuille and cylindrical Couette flows. Particularly, it is found that the precision of the present scheme can be greatly improved with the nonequilibrium distribution functions of two directions included. Three more test cases of particle-laden flow, including particle migration in a channel, the sedimentation of a particle under gravity and the drafting-kissing-tumbling (DKT) dynamics of two settling particles, further demonstrate the feasibility and accuracy of the present scheme.