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## Particulate Flow Simulation via a Boundary Condition-Enforced Immersed Boundary-Lattice Boltzmann Scheme (2009)

Citations: | 2 - 0 self |

### Citations

469 |
The Lattice Boltzmann Equation for Fluid Dynamics and Beyond
- Succi
- 2004
(Show Context)
Citation Context ... solving the N-S equations. As an alternative computational technique to N-S solvers, the lattice Boltzmann method (LBM) has achieved a great success in simulating various fluid flows in recent years =-=[18,19]-=-. LBM is a particle-based numerical scheme, which studies the dynamics of fictitious particles. Basically, it has two processes: streaming and collision. Themajor advantage of LBM is its simplicity, e... |

406 |
Lattice Boltzmann method for fluid flows
- Chen, Doolen
- 1998
(Show Context)
Citation Context ... solving the N-S equations. As an alternative computational technique to N-S solvers, the lattice Boltzmann method (LBM) has achieved a great success in simulating various fluid flows in recent years =-=[18,19]-=-. LBM is a particle-based numerical scheme, which studies the dynamics of fictitious particles. Basically, it has two processes: streaming and collision. Themajor advantage of LBM is its simplicity, e... |

365 |
The immersed boundary method
- Peskin
(Show Context)
Citation Context ... actual implementation, δ(x−XB(s,t)) is smoothly approximated by a continuous kernel distribution δ(x−XB (s,t))= Dij ( xij−XlB ) =δ ( xij−XlB ) δ ( yij−YlB ) , (2.14) where δ(r) is proposed by Peskin =-=[33]-=- δ(r)= 1 4h ( 1+cos (pir 2 )) , |r|62, 0, |r|>2; (2.15) h is the mesh spacing of Eulerian mesh around the boundary. Using Eq. (2.14), the velocity correction at Eulerian points can be expressed a... |

324 |
Numerical Analysis of Blood Flow in the Heart
- Peskin
- 1977
(Show Context)
Citation Context ...alized Galerkin finite element scheme is incorporated into DLM/FD method. The immersed boundary method (IBM) may be the simplest approach in the fixed mesh category. It was first introduced by Peskin =-=[8]-=- to model the blood flow in the human heart. This method uses a fixed Cartesian mesh to represent fluid phase, which is composed of Eulerian points. For the boundary immersed in the fluid, a set of La... |

133 |
1994b Numerical simulations of particulate suspensions via a discretized boltzmann equation. Part 2. Numerical results
- Ladd
(Show Context)
Citation Context ...rallel nature. No differential equation and resultant algebraic equation system are involved in the LBM. This approach has also been adopted to study particulate flows. Such work can be found in Ladd =-=[20, 21]-=-, Behrend [22], Aidun et al. [23], and Qi [24]. The interactions between fluid and particle are implemented through the bounce back rule in LBM. Although the LBM utilizes a fixed Cartesian mesh in par... |

124 | A distributed lagrange multiplier/fictitious domain method for particulate flows
- Glowinski, Pan, et al.
- 1999
(Show Context)
Citation Context ...he particle motion is required. One popular approach in the fixed mesh category is the class of distributed Lagrange multiplier/fictitious domain (DLM/FD) method which was proposed by Glowinski et al =-=[4, 5]-=-. The basic idea of DLM/FD method is to view the particle region as a fictitious domain. A distributed Lagrange multiplier is imposed to enforce the constraints of rigid-body motion to the fictitious ... |

110 | Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations
- Fadlun, Verzicco, et al.
(Show Context)
Citation Context ...straint force into the N-S equations to enforce rigid particle motion. The constraint force is determined by the penalty method. Using the direct forcing scheme, which was introduced by Fadlun et al. =-=[11]-=-, Uhlmann [12] presented an improved immersed boundary method, which greatly suppresses the force oscillations, to simulate flow around suspended rigid particles. An enhanced version of direct forcing... |

82 |
On pressure and velocity boundary conditions for the lattice Boltzmann BGK model,” Phys
- Zou, He
- 1997
(Show Context)
Citation Context ...articles are 1.0g/cm3 and the viscosity of fluid is 0.01g/(cm·s). The pressure difference between the inlet and outlet is 541 Pa. Hence, a pressure boundary condition which was proposed by Zou and He =-=[38]-=- J. Wu and C. Shu / Commun. Comput. Phys., 7 (2010), pp. 793-812 807 X Y 0 1 2 0 1 2 3 4 5 6 7 8 Initial Position (t=0s) Drafting (t=1s) Kissing (t=1.5s) Tumbling (t=2.5s) Figure 7: Sedimentation of t... |

80 | An Immersed Interface Method for the NavierStokes Equations with Singular Forces
- Li, Lai
- 2001
(Show Context)
Citation Context ...te spherical particle sedimentation. A nonlinear weighted technique and boundary point classification strategy at the immersed boundary are introduced to modify the velocity near the body. Li and Lai =-=[14]-=- applied the immersed interface method (IIM), which introduces the jump conditions for the velocity and pressure across the interface, to simulate the fixed and moving interface problems. Compared to ... |

68 | Lattice-Boltzmann simulations of particle-fluid suspensions - Ladd, Verberg - 2001 |

67 |
Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 2. Couette and Poiseuille flows
- Feng, Hu, et al.
- 1995
(Show Context)
Citation Context ... the particulate flows efficiently. To assess this capability, the motion of a single neutrally buoyant circular particle in linear shear flow is investigated. This problem was studied by Feng et al. =-=[34]-=- using finite element method. They found that the particle always transfers to the center of channel, independent of its initial position and velocity. Recently, this problem was also studied by Feng ... |

63 |
An immersed boundary method with direct forcing for the simulation of particulate flows
- Uhlmann
- 2005
(Show Context)
Citation Context ...into the N-S equations to enforce rigid particle motion. The constraint force is determined by the penalty method. Using the direct forcing scheme, which was introduced by Fadlun et al. [11], Uhlmann =-=[12]-=- presented an improved immersed boundary method, which greatly suppresses the force oscillations, to simulate flow around suspended rigid particles. An enhanced version of direct forcing scheme was pr... |

62 | Direct simulation of flows of solid-liquid mixtures - Hu - 1996 |

59 |
Discrete lattice effects on the forcing term in the lattice Boltzmann method, Phys
- Guo, Zheng, et al.
(Show Context)
Citation Context ...zmann equation. In order to correctly recover Eqs. (2.1) and (2.2) in the lattice Boltzmann frame, the contribution of the force density to both momentum ρu and momentum flux ρuu should be considered =-=[30, 31]-=-. Here, the LBE proposed by Guo et al. [31] is employed fα (x+eαδt,t+δt)− fα (x,t)=− 1 τ ( fα (x,t)− f eqα (x,t) ) +Fαδt, (2.5) Fα = ( 1− 1 2τ ) wα ( eα−u c2s + eα ·u c4s eα ) ·f, (2.6) ρu=∑ α eα fα+ ... |

41 |
A fast numerical method for solving the three-dimensional Stokes equations in the presence of suspended particles
- Fogelson, Peskin
- 1988
(Show Context)
Citation Context ...okes (N-S) equations with a body force are solved over the whole fluid-boundary domain. This approach can be efficiently applied to simulate flows with complex geometry. Recently, Fogelson and Peskin =-=[9]-=- indicated that IBM could also be applied to simulate flows involving suspended particles. Since then, many variants of IBM for particulate flow simulation have been presented. Based on the idea in [9... |

36 | An immersed interface method for viscous incompressible flows involving rigid and flexible boundaries
- Le, Khoo, et al.
(Show Context)
Citation Context ...to IBM with the first-order accurate delta function, the second-order accuracy can be obtained in IIM. J. Wu and C. Shu / Commun. Comput. Phys., 7 (2010), pp. 793-812 795 Employing the IIM, Le et al. =-=[15]-=- successfully simulated flows around both rigid and elastic moving objects. Recently, an extended IBM named immersed finite element method (IFEM) has been proposed [16, 17]. Applying finite element te... |

36 |
Nonlinear mechanics of fluidization of beds of spherical particles
- Fortes, Joseph, et al.
- 1987
(Show Context)
Citation Context ... surface is represented by 50 Lagrangian points with uniform distribution. It is known that the two particles settled close to each other would go through drafting, kissing and tumbling or DKT motion =-=[36]-=-. In Fig. 7, the results of present computation show the positions of two particles at several different time stages. From the figure, the clear DKT motion is demonstrated. The instantaneous vorticity... |

32 |
Direct analysis of particulate suspensions with inertia using the discrete boltzmann equation
- Aidun, Lu, et al.
- 1998
(Show Context)
Citation Context ...on and resultant algebraic equation system are involved in the LBM. This approach has also been adopted to study particulate flows. Such work can be found in Ladd [20, 21], Behrend [22], Aidun et al. =-=[23]-=-, and Qi [24]. The interactions between fluid and particle are implemented through the bounce back rule in LBM. Although the LBM utilizes a fixed Cartesian mesh in particulate flow simulation, the imp... |

29 | Direct simulations of 2D fluid-particle flows in biperiodic domains - Maury - 1999 |

28 |
The immersed boundary-lattice Boltzmann method for solving fluid particles interaction problems
- Feng, Michaelides
(Show Context)
Citation Context ...ilar to themoving meshmethod. To ease the coupling between the boundary and the flow domain, the idea of IBM is worthwhile to be incorporated into LBM. The first attemptwasmade by Feng andMichaelides =-=[25,26]-=-. The simulation of 2D and 3D particle sedimentation was carried out. Niu et al. [27] put forward a momentum exchange-based IB-LBM to simulate flows around fixed and moving particles. It is well known... |

26 |
The atomic-scale finite element method.
- Liu, Huang, et al.
- 2004
(Show Context)
Citation Context ...95 Employing the IIM, Le et al. [15] successfully simulated flows around both rigid and elastic moving objects. Recently, an extended IBM named immersed finite element method (IFEM) has been proposed =-=[16, 17]-=-. Applying finite element technique to both fluid and object domains, the immersed body can be handled more appropriately and accurately. One advantage of this method is to effectively model deformabl... |

23 | Proteus: a direct forcing method in the simulations of particulate flows - Feng, Michaelides - 2005 |

18 |
Navier-Stokes simulation with constraint forces: finitedifference method for particle-laden flows and complex geometries
- Höfler
(Show Context)
Citation Context ...ld also be applied to simulate flows involving suspended particles. Since then, many variants of IBM for particulate flow simulation have been presented. Based on the idea in [9], Hfler and Schwarzer =-=[10]-=- proposed a finite-difference method for particle-laden flows by adding a constraint force into the N-S equations to enforce rigid particle motion. The constraint force is determined by the penalty me... |

16 |
Lattice-Boltzmann simulation of particles in non-zero-Reynolds-number flows
- Qi
- 1999
(Show Context)
Citation Context ...ant algebraic equation system are involved in the LBM. This approach has also been adopted to study particulate flows. Such work can be found in Ladd [20, 21], Behrend [22], Aidun et al. [23], and Qi =-=[24]-=-. The interactions between fluid and particle are implemented through the bounce back rule in LBM. Although the LBM utilizes a fixed Cartesian mesh in particulate flow simulation, the implementation o... |

12 |
Solid boundaries in particle suspension simulations via lattice Boltzmann method , Phys
- Behrend
- 1995
(Show Context)
Citation Context ...differential equation and resultant algebraic equation system are involved in the LBM. This approach has also been adopted to study particulate flows. Such work can be found in Ladd [20, 21], Behrend =-=[22]-=-, Aidun et al. [23], and Qi [24]. The interactions between fluid and particle are implemented through the bounce back rule in LBM. Although the LBM utilizes a fixed Cartesian mesh in particulate flow ... |

12 | Direct numerical simulation of particulate flow via multigrid FEM techniques and the fictitious boundary method
- Wan, Turek
- 2006
(Show Context)
Citation Context .... Wu and C. Shu / Commun. Comput. Phys., 7 (2010), pp. 793-812 805 time L o n g it u d in a l c o o rd in a te o f p a rt ic le c e n te r, y p 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6 Present Wan and Turek =-=[35]-=- time L o n g it u d in a l v e lo c it y o f p a rt ic le c e n te r, v p 0 0.2 0.4 0.6 0.8 1 -8 -6 -4 -2 0 2 Present Wan and Turek [35] (a) (b) time R e p 0 0.2 0.4 0.6 0.8 1 0 5 10 15 20 25 Present... |

9 | A distributed Lagrange multiplier/fictitious domain method for viscoelastic particulate flows
- Singh, Joseph, et al.
- 2000
(Show Context)
Citation Context ...luid flow containing many rigid particles was successfully simulated by Glowinski et al [4,5]. Recently, the DLM/FD method has also been extended to simulate particulate flows in non-Newtonian fluids =-=[6, 7]-=-. Usually, the generalized Galerkin finite element scheme is incorporated into DLM/FD method. The immersed boundary method (IBM) may be the simplest approach in the fixed mesh category. It was first i... |

9 | A novel immersed boundary velocity correction–lattice boltzmann method and its application to simulate flow past a circular cylinder - Shu, Liu, et al. |

8 |
Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications
- Wu, Shu
(Show Context)
Citation Context ...due to mass exchange may lead to a force error, which would influence the solution of force on the object. To satisfy the non-slip boundary condition, we developed a boundary conditionenforced IB-LBM =-=[29]-=- recently. Following the idea of Shu et al. [28], the restoring force is set as unknown rather than pre-calculated. By enforcing the non-slip boundary condition, the unknown restoring force is determi... |

7 | A momentum exchange-based immersed boundary-lattice Boltzmann method for simulating incompressible viscous flows, Phys
- Niu, Shu, et al.
(Show Context)
Citation Context ...ain, the idea of IBM is worthwhile to be incorporated into LBM. The first attemptwasmade by Feng andMichaelides [25,26]. The simulation of 2D and 3D particle sedimentation was carried out. Niu et al. =-=[27]-=- put forward a momentum exchange-based IB-LBM to simulate flows around fixed and moving particles. It is well known that the restoring force calculation is an important task in IB-LBM. In general, the... |

4 |
2004a Lattice Boltzmann simulation on particle suspensions in a two-dimensional symmetric stenotic artery
- Li, Fang, et al.
(Show Context)
Citation Context ... of flow is of great interest in medical science. There are numerous papers on the study of the pulsatile flow in a mildly or severely stenotic artery. Recently, such problem was studied by Li et al. =-=[37]-=- employing LBM. As shown in Fig. 11, this system is a two-dimensional rigid planar channel with length L = 32d and width W = 8d, where d is the diameter of the rigid circular particles. The stenosis i... |

3 |
A modified immersed boundary method for simulations of fluid-particle interactions
- Luo, Wang, et al.
- 2007
(Show Context)
Citation Context ...d immersed boundary method, which greatly suppresses the force oscillations, to simulate flow around suspended rigid particles. An enhanced version of direct forcing scheme was proposed by Luo et al. =-=[13]-=- recently to simulate spherical particle sedimentation. A nonlinear weighted technique and boundary point classification strategy at the immersed boundary are introduced to modify the velocity near th... |

1 | Direct numerical simulations of fluid-solid systems using the arbitrary Lagrangian-Eulerian technique - Zhu - 2001 |

1 |
Viscoelastic mobility of a system of particles
- Yu, Phan-Thien, et al.
- 2002
(Show Context)
Citation Context ...luid flow containing many rigid particles was successfully simulated by Glowinski et al [4,5]. Recently, the DLM/FD method has also been extended to simulate particulate flows in non-Newtonian fluids =-=[6, 7]-=-. Usually, the generalized Galerkin finite element scheme is incorporated into DLM/FD method. The immersed boundary method (IBM) may be the simplest approach in the fixed mesh category. It was first i... |

1 |
Extended immersed boundarymethod using FEM
- Liu
- 2004
(Show Context)
Citation Context ...95 Employing the IIM, Le et al. [15] successfully simulated flows around both rigid and elastic moving objects. Recently, an extended IBM named immersed finite element method (IFEM) has been proposed =-=[16, 17]-=-. Applying finite element technique to both fluid and object domains, the immersed body can be handled more appropriately and accurately. One advantage of this method is to effectively model deformabl... |

1 |
Lattice BGKmodel forNavier-Stokes equation, Europhys
- Qian, d’Humieres, et al.
- 1992
(Show Context)
Citation Context ...e; τ is the single relaxation time; eα is the particle velocity; wα are coefficients which depend on the selected lattice; f is the force density acting on the fluid field. For the popular D2Q9 model =-=[32]-=-, the lattice velocity set is given by eα = 0 α=0, (cos[(α−1)pi/2],sin[(α−1)pi/2]) α=1,2,3,4, √ 2(cos[(α−5)pi/2+pi/4],sin[(α−5)pi/2+pi/4]) α=5,6,7,8. (2.8) And the corresponding equilibrium d... |