#### DMCA

## Link-wise Artificial Compressibility Method

### Citations

506 |
2001. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond
- Succi
(Show Context)
Citation Context ... [6, 7]. Both (a) the need of a dedicated solver for the pressure Poisson equation and 4 (b) the use of compact multi-dimensional interpolations, can be overcome by the lattice Boltzmann method (LBM) =-=[8]-=-, while preserving the main features of the Cartesian cut-cell method for mesh generation and boundary treatment. However, this comes at a price of dealing with specific features inherited from the ki... |

335 | A Numerical Method for Solving Incompressible Viscous Flow Problems - Chorin - 1967 |

190 |
Lattice BGK models for NavierStokes equation
- Qian, d’Humieres, et al.
- 1992
(Show Context)
Citation Context ...re no clear and general recipes yet, on how to optimally design ghost quantities with desired stability properties. As far as the popular compact stencils are concerned, such as D2Q9, D3Q15 and D3Q19 =-=[9]-=- with no special corrections, LBM ghost quantities remain numerical artifacts: Positive effects of such quantities for enhancing stability of usual FD schemes are still far from being clearly demonstr... |

117 |
Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, and stability, Phys
- Lallemand, Luo
(Show Context)
Citation Context ...ulation (see the end of Section 2.1 where this formulation is presented), standard (second-order) ACM and multiplerelaxation-time (MRT) LBM. The standard ACM is described in Ref. [13]. In the MRT-LBM =-=[14, 21]-=-, the consistent treatment of forcing is based on Ref. [19]. The time step employed in the LBM computation is the same as the one of ACM, i.e. Ma = 2piKn or equivalently ∆t = 2, and the tuning parame... |

100 | MultipleRelaxation-Time Lattice Boltzmann Models in Three Dimensions
- d‘Humières, Ginzburg, et al.
- 2002
(Show Context)
Citation Context ... the latter shifted grids. 30 Table 5 2D lid driven cavity flow at Re = 5000: Comparison between the present LWACM (with Mach number Ma = 0.2, ν = νp) and alternative solvers for INSE from literature =-=[13, 33, 8, 30, 31]-=-. In artificial compressibility methods (LW-ACM, BGK-LBM, MRT-LBM), even steady state solutions depend on the numerical Mach number: Hence a fair comparison among different methods requires using the ... |

91 | An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries
- Ye, Mittal, et al.
- 1999
(Show Context)
Citation Context ...e flow can be simply ignored during computations [2]. In the literature, this approach is typically referred to as the “embedded boundary method”, the “Cartesian grid method” or the “cut-cell method” =-=[3, 4, 5, 6, 7]-=-. Clearly, the challenging point is to make the method accurate in dealing with curved and planar boundaries transversal to the grid, even though such boundaries are conveniently approximated in a sta... |

59 |
Momentum transfer of a Boltzmann-lattice fluid with boundaries
- Bouzidi, Firdaouss, et al.
- 2001
(Show Context)
Citation Context ... the combination of previous steps yields fBB(i)(x̂, t̂+ 1) = f (e) i (x̂, t̂) + ( 2− 2 ω ) 2f (e,o) BB(i)(x̂, t̂). (17) In case of moving complex boundary with velocity uw, the procedure reported in =-=[24]-=- (here reformulated in terms of f (e,o) BB(i)) suggests the inclusion of the additional term δfBB(i)(ρ0,uw) = 2f (e,o) BB(i)(ρ0,uw), (18) where f (e,o) BB(i) is given by Eq. (2) and ρ0 is the averaged... |

53 |
A locally refined rectangular grid finite element method: application to computational fluid dynamics and computational physics
- Young, Melvin, et al.
- 1990
(Show Context)
Citation Context ...e flow can be simply ignored during computations [2]. In the literature, this approach is typically referred to as the “embedded boundary method”, the “Cartesian grid method” or the “cut-cell method” =-=[3, 4, 5, 6, 7]-=-. Clearly, the challenging point is to make the method accurate in dealing with curved and planar boundaries transversal to the grid, even though such boundaries are conveniently approximated in a sta... |

51 |
The 2D lid-driven cavity problem revisited.
- CH
- 2007
(Show Context)
Citation Context ...1 2D lid driven cavity flow In this section, the effective enhanced stability of the present LW-ACM method is tested by means of the classical two-dimensional (2D) lid driven cavity problem (see also =-=[33, 37]-=-). Such a benchmark has been considered owing to a singularity of the pressure in the lid corners, which makes it a severe test for robustness of numerical schemes, especially starting from moderately... |

47 |
Grid Generation Methods.
- Liseikin
- 1999
(Show Context)
Citation Context ...rmulas 53 F Appendix: Asymptotic analysis for energy equation 57 3 1 Introduction Despite a large variety of mesh generation techniques for numerical solvers of the fluid dynamics governing equations =-=[1]-=-, addressing complex geometries remains a difficult duty. To this aim, several approaches were proposed for adapting computational grids to complex geometries by unstructured meshes. Generating unstru... |

47 | Asymptotic Analysis of the Lattice Boltzmann Equation
- Junk, Klar, et al.
(Show Context)
Citation Context ...SE), in addition to an artificial continuity equation including pressure time derivative. ACE can be also recovered by the more systematic expansion such as the Hilbert method under diffusive scaling =-=[11]-=-. The lattice kinetic scheme (LKS) [12] (a variant of LBM) also shows similarities with ACM at the level of computer programming, despite the fact that the former deals with distribution functions of ... |

46 | On the single processor performance of simple lattice bolzmann kernels.
- Wellein, Zeiser, et al.
- 2006
(Show Context)
Citation Context ...anks to an optimized implementation of the algorithm (3) and (5). Similarly to LBM, the performance characteristics of single-processor implementations depends on the effect of different data layouts =-=[17]-=- (multiprocessor optimization strategies are not considered in the present work, see Ref. [18]). First of all, the streaming step should not overwrite data required for updating neighboring sites. A u... |

43 | Performance of under-resolved two-dimensional incompressible flow simulations
- MINION, BROWN
- 1997
(Show Context)
Citation Context ...apabilities are demonstrated (compared to BGK-LBM). From a computational point of view, Table 2 Performance test of the link-wise ACM (by FD formulation) vs. BGK-LBM, based on the Minion & Brown flow =-=[22]-=- with Re = 10, 000 in the time range t ∈ [0, 1], solved by a mesh with 512×512 nodes/sites and performing 12,800 iterations (Ma = 0.04). Both codes are serial and use double precision. The considered ... |

41 |
Introduction to High Performance Computing for Scientists and Engineers
- Hager, Wellein
- 2010
(Show Context)
Citation Context ...mance characteristics of single-processor implementations depends on the effect of different data layouts [17] (multiprocessor optimization strategies are not considered in the present work, see Ref. =-=[18]-=-). First of all, the streaming step should not overwrite data required for updating neighboring sites. A usual way to work around the resulting data dependencies owing to the propagation step is the u... |

40 |
Theory of the Lattice Boltzmann Method: Acoustic and Thermal Properties in Two and Three Dimensions”, Physical Review E,
- Lallemand, Luo
- 2003
(Show Context)
Citation Context ...e domain of interest, with the quantities f (e)i defined such that p = ρ T/3. There were a number of suggestions aiming at enabling thermal fluid-dynamic simulations with the lattice Boltzmann method =-=[32]-=-. Among the most interesting ones, we remind: (a) Increase of the number of velocities and inclusion of higher-order nonlinear terms (in flow velocity) in the equilibrium distribution functions; (b) i... |

18 | A representation of curved boundaries for the solution of the navier-stokes equations on a staggered three-dimensional cartesian grid
- Kirkpatrick, Armfield, et al.
(Show Context)
Citation Context ...omputational molecules, and problems associated with the transfer of information across grid interfaces. The added complexity makes code development even more difficult and increases computation time =-=[2]-=-, with an additional risk that those algorithms may not lead to an acceptable solution. An alternative approach which has attracted an increasing interest in recent years makes use of Cartesian grids ... |

13 | Generalized Lattice Boltzmann Equations - d‘Humières - 1992 |

13 |
Bulk and shear viscosities in lattice Boltzmann equations
- Dellar
- 2001
(Show Context)
Citation Context ...l schemes for under-resolved simulations of the 2D incompressible NavierStokes equations. The relevance of this flow for testing robustness and accuracy of LBM schemes was first pointed out by Dellar =-=[23]-=-. Minion & Brown considered initial conditions corresponding to the perturbed shear layer 18 ū(t, x, y) = tanh(k(y − 1/4)), y ≤ 1/2,tanh(k(3/4− y)), y > 1/2, (12) v̄(t, x, y) = δ sin(2pi(x+ 1/4... |

12 |
A novel fully-implicit finite volume method 72 Copyright ©
- Sahin, RG
- 2003
(Show Context)
Citation Context ...1 2D lid driven cavity flow In this section, the effective enhanced stability of the present LW-ACM method is tested by means of the classical two-dimensional (2D) lid driven cavity problem (see also =-=[33, 37]-=-). Such a benchmark has been considered owing to a singularity of the pressure in the lid corners, which makes it a severe test for robustness of numerical schemes, especially starting from moderately... |

11 |
An adaptively refine Cartesian mesh solver for the Euler equation
- Zeeuw, Powell
- 1993
(Show Context)
Citation Context ...e flow can be simply ignored during computations [2]. In the literature, this approach is typically referred to as the “embedded boundary method”, the “Cartesian grid method” or the “cut-cell method” =-=[3, 4, 5, 6, 7]-=-. Clearly, the challenging point is to make the method accurate in dealing with curved and planar boundaries transversal to the grid, even though such boundaries are conveniently approximated in a sta... |

11 |
Nonhydrodynamic modes and a priori construction of shallow water lattice Boltzmann equations
- Dellar
(Show Context)
Citation Context ...ount for nonhydrodynamic quantities (sometimes called ghost quantities) which, though may not have direct impact on the hydrodynamic behavior, they can still be responsible of numerical instabilities =-=[16]-=-. Unfortunately, owing to nonlinearities, there are no clear and general recipes yet, on how to optimally design ghost quantities with desired stability properties. As far as the popular compact stenc... |

11 |
Numerical simulation of particular suspension via a discretized Boltzmann equation. Part 2: Numerical results
- Ladd
- 1994
(Show Context)
Citation Context ...lation is also very useful in computing hydrodynamical forces acting on bodies. A popular approach in LBM literature is based on the socalled momentum exchange algorithm (MEA), originally proposed in =-=[25]-=- and lately improved in [26] (see [27] for a complete discussion). In LBM, at every time step, the momentum pi = v̂if post i (x̂, t̂)− v̂BB(i)fBB(i)(x̂, t̂+ 1) = v̂i [ fposti (x̂, t̂) + fBB(i)(x̂, t̂+... |

7 | Developments in Cartesian cut cell methods.
- Ingram, Causon, et al.
- 2003
(Show Context)
Citation Context |

6 |
Connection between kinetic methods for fluid-dynamic equations and macroscopic finite-difference schemes
- Asinari, Ohwada
- 2009
(Show Context)
Citation Context ... 1, but Eq. (1) is also valid for tunable ω and consequently tunable viscosity ν (in particular, for high Reynolds number flows). Moreover, the same derivation can be done for the FD-LKSν proposed in =-=[20]-=-, but Eq. (1) is formulated only along a particular lattice link and hence it can also take advantage of most of LBM technology (which is link-wise). (1) Availability of two alternative formulations o... |

6 |
2007 Lattice Boltzmann method for thermal flow simulation on standard lattices
- Prasianakis, Karlin
(Show Context)
Citation Context ...rder nonlinear terms (in flow velocity) in the equilibrium distribution functions; (b) inclusion of finite difference corrections aiming at the fulfillment of energy conservation on standard lattices =-=[34]-=- and, (c) use of two sets of distribution functions for particle number density (fi), and energy density (gi), doubling the number of discrete velocities. Even though the first and the second approach... |

5 |
Lattice Boltzmann equation with multiple effective relaxation times for gaseous microscale flow.
- Guo, Zheng, et al.
- 2008
(Show Context)
Citation Context ...use a correction to the distribution function may affect the dynamics of the higher order moments as well. Consistent treatment of the forcing typically involves some special (non-trivial) techniques =-=[19]-=-. Details on the effects due to the correction (4), by asymptotic analysis, are reported in the Appendix C. Imposing a given physical acceleration ḡ within a flow, requires the tuning of numerical ac... |

5 | Numerics of the Lattice Boltzmann Method: Effects of Collision Models on the Lattice Boltzmann Simulations - Luo, Liao, et al. |

4 |
A lattice kinetic scheme for incompressible viscous flows with heat transfer
- Inamuro
(Show Context)
Citation Context ...nuity equation including pressure time derivative. ACE can be also recovered by the more systematic expansion such as the Hilbert method under diffusive scaling [11]. The lattice kinetic scheme (LKS) =-=[12]-=- (a variant of LBM) also shows similarities with ACM at the level of computer programming, despite the fact that the former deals with distribution functions of gas molecules, while the latter only wi... |

3 |
Generalized Maxwell State and H Theorem for Computing Fluid Flows using the Lattice Boltzmann Method, Phys
- Asinari, Karlin
(Show Context)
Citation Context ...(u2 + v2) , 44 where u and v are the velocity components, i.e. (u, v)T = u, with pressure being p = ρ/3. The above equations (A.1) and (A.3) can be generalized as follows =-=[35]-=- f (g) (Πxx,Πyy) = ρ (1− Πxx) (1− Πyy) , ρ (Πxx + u) (1− Πyy) /2, ρ (Πxx − u) (1− Πyy) /2, ρ (1− Πxx) (Πyy + v) /2, ρ (1− Πxx) (Πyy − v) /2, ρ (Πxx + u) (Πyy + v) /4, ρ (Π... |

2 | Artificial compressibility method revisited: Asymptotic numerical method for incompressible NavierStokes equations
- Ohwada, Asinari
(Show Context)
Citation Context ...iant of ACM. Recently, taking advantage of the similarities between LBM and ACM, the latter was reformulated as a high order accurate numerical method (fourth order in space and second order in time) =-=[13]-=-. Motivated by the common belief that an important reason of success of the LBM (in particular MRT-LBM [14]) is its remarkable robustness for simulating the various complex flows, the stability of the... |

2 |
Corrected momentum exchange method for lattice Boltzmann simulations of suspension flow
- Lorenz, Caiazzo, et al.
(Show Context)
Citation Context ...n computing hydrodynamical forces acting on bodies. A popular approach in LBM literature is based on the socalled momentum exchange algorithm (MEA), originally proposed in [25] and lately improved in =-=[26]-=- (see [27] for a complete discussion). In LBM, at every time step, the momentum pi = v̂if post i (x̂, t̂)− v̂BB(i)fBB(i)(x̂, t̂+ 1) = v̂i [ fposti (x̂, t̂) + fBB(i)(x̂, t̂+ 1) ] , (20) is transferred ... |

2 |
Three-dimensional flow in cavity at Yaw
- Povitsky
- 2001
(Show Context)
Citation Context ...Fig. 11) at Re = 2000. a) LW-ACM with 483 uniform grid. b) LW-ACM with 603 uniform grid. c) LW-ACM with 683 uniform grid. d) Reference solution by the commercial code FLUENT with 683 non-uniform grid =-=[29]-=-. where C = 1 re/ri − ri/re . (33) Here, ū, v̄, p̄ and T̄ denote horizontal velocity, vertical velocity, pressure and the torque on the inner cylinder respectively, with θ being the angle between rad... |

1 |
A three-dimensional Cartesian cut cell method for incompressible viscous flow with irregular domains
- Luo, Gu, et al.
- 2011
(Show Context)
Citation Context |

1 | Artificial compressibility method and lattice Boltzmann method: Similarities and differences Comput
- Ohwada, Asinari, et al.
- 2011
(Show Context)
Citation Context ...n important reason of success of the LBM (in particular MRT-LBM [14]) is its remarkable robustness for simulating the various complex flows, the stability of the revived ACM has been further enhanced =-=[15]-=-. In this paper, in an attempt of making ACM even more similar to LBM, we propose yet a new formulation of ACM referred to as link-wise ACM (LWACM) in the following text. For the sake of completeness,... |

1 |
thesis, Scuola Normale Superiore
- Caiazzo
- 2007
(Show Context)
Citation Context ...g hydrodynamical forces acting on bodies. A popular approach in LBM literature is based on the socalled momentum exchange algorithm (MEA), originally proposed in [25] and lately improved in [26] (see =-=[27]-=- for a complete discussion). In LBM, at every time step, the momentum pi = v̂if post i (x̂, t̂)− v̂BB(i)fBB(i)(x̂, t̂+ 1) = v̂i [ fposti (x̂, t̂) + fBB(i)(x̂, t̂+ 1) ] , (20) is transferred from the f... |

1 |
High-incidence 3-D Lid-driven Cavity Flow
- Povitsky
- 2001
(Show Context)
Citation Context ...C.10)). Here, we have chosen the three-dimensional (3D) diagonally lid-driven cavity flow, which is a classical benchmark for numerical solvers of the incompressible Navier-Stokes equations (see also =-=[28, 30, 29]-=-). The cavity is a cubic box with unit edge as schematically sketched in Fig. 11. The boundary condition at the top plane (x, y, 1) is uL = ( √ 2, √ 2, 0)/20 so that uL = ‖uL‖ = 1/10, whereas the rema... |

1 | Localization of Hopf bifurcations in fluid flow problems - Jervais - 1997 |