We study the settling of solid particles within a viscous incompressible fluid contained in a two-dimensional channel, where the mass density of the particles is slightly greater than that of the fluid. The fluid-structure interaction problem is simulated numerically using the immersed boundary method, with an added mass term that is incorporated using a Boussinesq approximation. Simulations are performed with a single circular particle, and also with two particles in various initial configurations. The terminal settling velocities for the particles correspond closely with both theoretical and experimental results, and the single-particle dynamics reproduce expected behavior qualitatively. The two-particle simulations exhibit drafting-kissing-tumbling dynamics that is similar to what is observed in other experimental and numerical studies.
The gravity-driven motion of rigid particles in a viscous fluid is relevant in many natural and industrial processes, yet this has mainly been investigated for spherical particles. We therefore consider the sedimentation of non-spherical (spheroidal) isolated and particle pairs in a viscous fluid via numerical simulations using the Immersed Boundary Method. The simulations performed here show that the critical Galileo number for the onset of secondary motions decreases as the spheroid aspect ratio departs from 1. Above this critical threshold, oblate particles perform a zigzagging motion where…
Sedimentation of a dispersed solid phase is widely encountered in applications and environmental flows, yet little is known about the behavior of finite-size particles in homogeneous isotropic turbulence. To fill this gap, we perform Direct Numerical Simulations of sedimentation in quiescent and turbulent environments using an Immersed Boundary Method to account for the dispersed rigid spherical particles. The solid volume fractions considered are 0.5-1%, while the solid to fluid density ratio 1.02. The particle radius is chosen to be approximately 6 Komlogorov lengthscales. The results show t…
In our recent work [H. Zhang, F.X. Trias, A. Oliva, D. Yang, Y. Tan, Y. Sheng. PIBM: Particulate immersed boundary method for fluid-particle interaction problems. Powder Technology. 272(2015), 1-13.], a particulate immersed boundary method (PIBM) for simulating fluid-particle multiphase flow was proposed and assessed in both two- and three-dimensional applications. In this study, the PIBM was extended to solve thermal interaction problems between spherical particles and fluid. The Lattice Boltzmann Method (LBM) was adopted to solve the fluid flow and temperature fields, the PIBM was responsibl…
We present an improved method for computing incompressible viscous flow around suspended rigid particles using a fixed and uniform computational grid. The main idea is to incorporate Peskin's regularized delta function approach [Acta Numerica 11 (2002) 1] into a direct formulation of the fluid-solid interaction force in order to allow for a smooth transfer between Eulerian and Lagrangian representations while at the same time avoiding strong restrictions of the time step. This technique was implemented in a finite-difference and fractional-step context. A variety of two- and three-dimensional …
The sedimentation of a rigid particle near a wall in a viscous fluid has been studied numerically by many authors, but analytical solutions have been derived only for special cases such as the motion of spherical particles. In this paper the method of images is used to derive simple ordinary differential equations describing the sedimentation of arbitrarily oriented prolate and oblate spheroids at zero Reynolds number near a vertical or inclined plane wall. The differential equations may be solved analytically in many situations, and full trajectories are predicted which compare favorably with…
The present study reports on flow past airfoils (stationary and moving) using sharp interface immersed-boundary approach. Non-boundary conforming approach like immersed-boundary method offers a viable alternative over traditional boundary conforming approach by allowing us to model flow past arbitrarily complex shapes, by eliminating the need to re-grid the flow domain as the body exhibits motion. We present flow past a NACA 0012 airfoil at stationary conditions as well as exhibiting pitching motion. Evolution of vortex dynamics and wake structures are presented to show that the developed shar…
A new formulation of the immersed boundary method, which facilitates accurate simulation of incompressible isothermal and natural convection flows around immersed bodies and which may be applied for accurate linear stability analysis of the flows, is presented. The method is based on the fully pressure-velocity coupled approach, implicitly satisfying the divergence-free velocity constraint with no need for an extra projection-correction step, which is a significant advantage for the computational efficiency. The method treats pressure, boundary forces, and heat sources as Lagrange multipliers,…
We present a strongly-coupled immersed-boundary method for flow-structure interaction problems involving thin deforming bodies. The method is stable for arbitrary choices of solid-to-fluid mass ratios and for large body motions. As with many strongly-coupled immersed-boundary methods, our method requires the solution of a nonlinear algebraic system at each time step. The system is solved through iteration, where the iterates are obtained by linearizing the system and performing a block LU factorization. This restricts all iterations to small-dimensional subsystems that scale with the number of…
An extended immersed boundary method utilizing a semi-implicit direct forcing approach for the simulation of confined incompressible viscous thermal flow problems is presented. The method utilizes a Schur complement approach to enforce the kinematic constraints of no-slip and the corresponding thermal boundary conditions for immersed surfaces. The developed methodology can be straightforwardly adapted to any existing incompressible time marching solver based on a segregated pressure-velocity coupling. The method accurately meets the thermal and the no-slip boundary conditions on the surfaces o…
In the present study, a discrete forcing Immersed Boundary Method (IBM) is proposed for the numerical simulation of high-speed flow problems including heat exchange. The flow field is governed by the compressible Navier-Stokes equations, which are resolved by using the open source library OpenFOAM. The numerical solver is modified to include source terms in the momentum equation and in the energy equation, which account for the presence of the immersed body. The method is validated on some benchmark test cases dealing with forced convection problems and moving immersed bodies. The results obta…
Modelling the vascular transport and adhesion of man-made particles is crucial for optimizing their efficacy in the detection and treatment of diseases. Here, a Lattice Boltzmann and Immersed Boundary methods are combined together for predicting the near wall dynamics of particles with different shapes in a laminar flow. For the lattice Boltzmann modelling, a Gauss-Hermite projection is used to derive the lattice equation, wall boundary conditions are imposed through the Zou-He framework, and a moving least squares algorithm accurately reconstructs the forcing term accounting for the immersed …
It is well known that the number of particles should be scaled up to enable industrial scale simulation. The calculations are more computationally intensive when the motion of the surrounding fluid is considered. Besides the advances in computer hardware and numerical algorithms, the coupling scheme also plays an important role on the computational efficiency. In this study, a particle immersed boundary method (PIBM) for simulating the fluid-particle multiphase flow was presented and assessed in both two- and three-dimensional applications. The idea behind PIBM derives from the conventional mo…
The immersed boundary method (IB) is an elegant way to fully couple the motion of a fluid and deformations of an immersed elastic structure. In that vein, the IB2d software allows for expedited explorations of fluid-structure interaction for beginners and veterans to the field of computational fluid dynamics (CFD). While most open source CFD codes are written in low level programming environments, IB2d was specifically written in high- level programming environments to make its accessibility extend beyond scientists with vast programming experience. Although introduced previously by Battista e…
We describe an immersed boundary method in which the fluid-structure coupling is achieved in an Eulerian framework. The method is an improved extension of the immersed boundary method originally developed by Kajishima et al. [1], which accounts for the inertia of the fictitious fluid inside the particle volume and is thus able to reproduce the behaviour of particles both in the case of neutrally-buoyant objects and in the presence of density difference between the particles and the fluid. The method is capable to handle the presence of multiple suspended objects, i.e., a suspension, by includi…
Mesh Adaptation on Hybrid Unstructured Meshes for Immersed Boundary Methods
School of Aeronautics, Universidad Politécnica de Madrid（马德里理工大学航空学院）；Center for Computational Simulation, Universidad Politécnica de Madrid（马德里理工大学计算模拟中心）
Particle sedimentation in the vicinity of a fixed horizontal vortex with time-dependent intensity can be chaotic, provided gravity is sufficient to displace the particle cloud while the vortex is off or weak. This "stretch, sediment and fold" mechanism is close to the so-called blinking vortex effect, which is responsible for chaotic transport of perfect tracers, except that in the present case the vortex motion is replaced by gravitational settling. In the present work this phenomenon is analyzed for heavy Stokes particles moving under the sole effect of gravity and of a linear drag. The vort…
A new parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. Immersed surfaces with prescribed motions are generated using the interpolation and regularization operators obtained from the discrete delta function approach of the original (Peskin's) immersed boundary method. Unlike Peskin's method, boundary forces are regarded as Lagrange multipliers that are used to satisfy the no-slip condition. The incompressible Navier-Stokes equations are discretized on an unbounded staggered Cartesian grid…
We present a fully Eulerian hybrid immersed-boundary/phase-field model to simulate wetting and contact line motion over any arbitrary geometry. The solid wall is described with a volume-penalisation ghost-cell immersed boundary whereas the interface between the two fluids by a diffuse-interface method. The contact line motion on the complex wall is prescribed via slip velocity in the momentum equation and static/dynamic contact angle condition for the order parameter of the Cahn-Hilliard model. This combination requires accurate computations of the normal and tangential gradients of the scalar…
We consider the motion of a fluid-immersed negatively buoyant particle in the vicinity of a thin compressible elastic wall, a situation that arises in a variety of technological and natural settings. We use scaling arguments to establish different regimes of sliding, and complement these estimates using thin-film lubrication dynamics to determine an asymptotic theory for the sedimentation, sliding, and spinning motions of a cylinder. The resulting theory takes the form of three coupled nonlinear singular-differential equations. Numerical integration of the resulting equations confirms our scal…
A conjugate heat transfer (CHT) immersed boundary (IB and CHTIB) method is developed for use with laminar and turbulent flows with low to moderate Reynolds numbers. The method is validated with the canonical flow of two co-annular rotating cylinders at $Re=50$ which shows second order accuracy of the $L_{2}$ and $L_{\infty}$ error norms of the temperature field over a wide rage of solid to fluid thermal conductivities, $κ_{s}/κ_{f} = \left(9-100\right)$. To evaluate the CHTIBM with turbulent flow a fully developed, heated, turbulent channel $\left(Re_{u_τ}=150\text{ and } κ_{s}/κ_{f}=4 \right)…
In this paper, the Immersed Boundary Method (IBM) proposed by Pinelli is implemented for finite volume approximations of incompressible Navier-Stokes equations solutions in the open source toolbox OpenFOAM version 2.2. Solid obstacles are described using a discrete forcing approach for boundary conditions. Unlike traditional approaches encompassing the presence of a solid body using conformal meshes and imposing no-slip boundary conditions on the boundary faces of the mesh, the solid body is here represented on the Eulerian Cartesian mesh through an ad-hoc body force evaluated on a set of Lagr…
Fully resolved simulation of flows with buoyant particles is a challenging problem since buoyant particles are lighter than the surrounding fluid, and as a result, the two phases are strongly coupled together. In this work, the virtual force stabilization technique introduced by Schwarz et al. [Schwarz, S., Kempe, T., & Fröhlich, J. (2015). A temporal discretization scheme to compute the motion of light particles in viscous flows by an immersed boundary method. J. Comput. Phys., 281, 591-613] is extended to simulate buoyant particle suspensions with high volume fractions (up to $40 \%$). It is…
Immersed boundary methods are extensively used for simulations of dynamic solid objects interacting with fluids due to their computational efficiency and modelling flexibility compared to body-fitted grid methods. However, thin geometries, such as shells and membranes, cause a violation of the boundary conditions across the surface for many immersed boundary projection algorithms. Using a one-dimensional analytical derivation and multi-dimensional numerical simulations, this manuscript shows that adjustment of the Poisson matrix itself is require to avoid large velocity, pressure, and force pr…
Handling geometric singularities efficiently with the immersed-boundary method: application to riblets
Institute of Fluid Mechanics, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院流体力学研究所）；Dept. of Aerospace Engineering, Politecnico di Milano（米兰理工大学航空航天工程系）；Dip. di Ingegneria Industriale, Università di Salerno（萨莱诺大学工业工程系）
We derive a mathematical model and the corresponding computational scheme to study deflection of a two-dimensional elastic cantilever beam immersed in a channel, where one end of the beam is fixed to the channel wall. The immersed boundary method has been employed to simulate numerically the fluid-structure interaction problem. We investigate how variations in physical and numerical parameters change the effective material properties of the elastic beam and compare the results qualitatively with linear beam theory. We also pay careful attention to "corner effects" -- irregularities in beam sha…
The study of viscous fluid flow coupled with rigid or deformable solids has many applications in biological and engineering problems, e.g., blood cell transport, drug delivery, and particulate flow. We developed a partitioned approach to solve this coupled Multiphysics problem. The fluid motion was solved by Palabos (Parallel Lattice Boltzmann Solver), while the solid displacement and deformation was simulated by LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). The coupling was achieved through the immersed boundary method (IBM). The code modeled both rigid and deformable so…
Comments on An implicit-Chebyshev pseudospectral method for the effect of radiation on power-law fluid past a vertical plate immersed in a porous medium, by N.S. Elgazery,CNSNS,2008
A second-order diffusive-interface immersed boundary method for incompressible flow with phase change and moving interfaces
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, College of Engineering, Peking University（北京大学工学院力学与工程科学系湍流与复杂系统国家重点实验室）；Department of Mechatronics Engineering, Morgan State University（摩根州立大学机电工程系）；Department of Mechanical Engineering, Johns Hopkins University（约翰斯·霍普金斯大学机械工程系）
In this paper, a novel immersed boundary method is developed, validated, and applied. Through devising a second-order three-step flow reconstruction scheme, the proposed method is able to enforce the Dirichlet, Neumann, Robin, and Cauchy boundary conditions in a straightforward and consistent manner. Equipped with a fluid-solid coupling framework that integrates high-order temporal and spatial discretization schemes, numerical experiments concerning flow involving stationary and moving objects, convex and concave geometries, no-slip and slip wall boundary conditions, as well as subsonic and su…
The fluid dynamics video considers an array of two NREL 5-MW turbines separated by seven rotor diameters in a neutral atmospheric boundary layer (ABL). The neutral atmospheric boundary-layer flow data were obtained from a precursor ABL simulation using a Large-Eddy Simulation (LES) framework within OpenFOAM. The mean wind speed at hub height is 8m/s, and the surface roughness is 0.2m. The actuator line method (ALM) is used to model the wind turbine blades by means of body forces added to the momentum equation. The fluid dynamics video shows the root and tip vortices emanating from the blades f…
An immersed-boundary (IB) method is proposed and applied in the gas-kinetic BGK scheme to simulate incompressible/compressible viscous flow with stationary/moving boundary. In present method the ghost-cell technique is adopted to fulfill the boundary condition on the immersed boundary. A novel idea "local boundary determination" is put forward to identify the ghost cells, each of which may have several different ghost-cell constructions corresponding to different boundary segments, thus eliminating the singularity of the ghost cell. Furthermore, the so-called "fresh-cell" problem when implemen…
In the first part of this study, 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 f…
The immersed boundary (IB) method is a general mathematical framework for studying problems involving fluid-structure interactions in which an elastic structure is immersed in a viscous incompressible fluid. In the IB formulation, the fluid described by Eulerian variables is coupled with the immersed structure described by Lagrangian variables via the use of the Dirac delta function. From a numerical standpoint, the Lagrangian force spreading and the Eulerian velocity interpolation are carried out by a regularized, compactly supported discrete delta function, which is assumed to be a tensor pr…
This paper introduces a new immersed boundary (IB) method for viscous incompressible flow, based on a Fourier spectral method for the fluid solver and on the nonuniform fast Fourier transform (NUFFT) algorithm for coupling the fluid with the immersed boundary. The new Fourier spectral immersed boundary (FSIB) method gives improved boundary resolution in comparison to the standard IB method. The interpolated velocity field, in which the boundary moves, is analytically divergence-free. The FSIB method is gridless and has the meritorious properties of volume conservation, exact translation invari…
A discrete unified gas kinetic scheme (DUGKS) coupled with the immersed boundary (IB) method is developed to perform interface-resolved simulation of particle-laden flows. The present method (IB-DUGKS) preserves the respective advantages of the IB and DUGKS, i.e., the flexibility and efficiency for treating complex flows, and the robustness and low numerical-dissipation. In IB-DUGKS, the IB method is used to treat the fluid-solid interfaces and the DUGKS is applied to simulate the fluid flow, making use of the Lagrangian and Eulerian meshes, respectively. Those two meshes are fully independent…
Two methods for solid body representation in flow simulations available in the Pencil Code are the immersed boundary method and overset grids. These methods are quite different in terms of computational cost, flexibility and numerical accuracy. We present here an investigation of the use of the different methods with the purpose of assessing their strengths and weaknesses. At present, the overset grid method in the Pencil Code can only be used for representing cylinders in the flow. For this task it surpasses the immersed boundary method in yielding highly accurate solutions at moderate comput…
The interpolated bounce-back scheme 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 bo…
This paper sums up some recent validations of an immersed boundary method for compressible flow simulations. It has been already shown that this method is able to provide accurate results without meshing effort around more or less complex geometries. Here, the authors focus on several simple test cases to assess the application range of the method. From subsonic to hypersonic flows, from steady to large-eddy unsteady simulations, in 2D or 3D, results are compared to classical simulations with body-fitted meshes and experiment. Moreover, the use of an efficient Navier-Stokes solver for all the …
In this paper, we propose an alternative approach to implement the contact angle boundary condition on immersed surfaces for phase-field simulations of two-phase flows using the Cahn-Hilliard equation on a Cartesian mesh. This simple and effective method was inspired by previous works on the geometric formulation of the wetting boundary condition. In two dimensions, by making full use of the hyperbolic tangent profile of the order parameter, we were able to obtain its unknown value at a ghost point from the information at only one point in the fluid. This is in contrast with previous approache…
The performance of a single or the collection of microswimmers strongly depends on the hydrodynamic coupling among their constituents and themselves. We present a numerical study for a single and a pair of microswimmers based on lattice Boltzmann method (LBM) simulations. Our numerical algorithm consists of two separable parts. Lagrange polynomials provide a discretization of the microswimmers and the lattice Boltzmann method captures the dynamics of the surrounding fluid. The two components couple via an immersed boundary method. We present data for a single swimmer system and our data also s…
The development of fluid-structure interaction (FSI) software involves trade-offs between ease of use, generality, performance, and cost. Typically there are large learning curves when using low-level software to model the interaction of an elastic structure immersed in a uniform density fluid. Many existing codes are not publicly available, and the commercial software that exists usually requires expensive licenses and may not be as robust or allow the necessary flexibility that in house codes can provide. We present an open source immersed boundary software package, IB2d, with full implement…
