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A Lattice Boltzmann-Direct Forcing/fictitious domain Model for Brownian Particles in Fluctuating Fluids

Communications in Computational Physics 2011年第4期9卷 959-973页

作者： Deming Nie Jianzhong Lin State Key Laboratory of Fluid Power Transmission and Control Zhejiang UniversityHangzhou 310027China College of Metrology and Technology Engineering China Jiliang UniversityHangzhou 310018China

The previously developed LB-DF/FD method derived from the lattice Boltzmann method and Direct Forcing/fictitious domain method is extended to deal with 3D particle’s Brownian *** the model the thermal fluctuations are introduced as random forces and torques acting on the Brownian *** hydrodynamic interaction is introduced by directly resolving the fluid motions.A sphere fluctuating in a cubic box with the periodic boundary is considered to validate the present *** examining the velocity autocorrelation function(VCF)and rotational velocity autocorrelation function(RVCF),it has been found that in addition to the two relaxation times,the mass density ratio should be taken into consideration to check the accuracy and effectiveness of the present ***,the fluctuation-dissipation theorem and equipartition theorem have been investigated for a single spherical ***,a Brownian particle trapped in a harmonic potential has been simulated to further demonstrate the ability of the LB-DF/FD model.

关键词： Lattice Boltzmann method fictitious domain Brownian motion

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A fictitious domain METHOD FOR DIRICHLET PROBLEM AND ITS APPLICATIONS TO GENER ALIZED STOKES PROBLEM

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Transactions of Nanjing University of Aeronautics and Astronautics 2001年第1期18卷 22-28页

作者：周春华唐海敏南京航空航天大学航空宇航学院

This paper discusses a fictitious domain method for the linear Dirichlet problem and its applications to the generalized Stokes problem. This method treats Dirichlet boundary condit ion via a Lagrange multiplier technique and is well suited to the no-slip bound ary condition in viscous flow problems. In order to improve the accuracy of solu tions, meshes are refined according to the a posteriori error estimate. The mini -element discretization is applied to solve the generalized Stokes problem. Fin ally, some numerical results to validate this method are presented for partial d ifferential equations with Dirichlet boundary condition.

关键词： fictitious domain Diri chlet problem finite element generalized Stokes problem Lagrange multiplier

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Numerical computations of the flow in a finite diverging channel

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2010年第1期11卷 50-60页

作者： Zhao-sheng YU Xue-ming SHAO Jian-zhong LIN State Key Laboratory of Fluid Power Transmission and Control Department of Mechanics Zhejiang University Hangzhou 31002 7 China

The flow in a finite diverging channel opening into a large space and resembling the experimental prototype of Putkaradze and Vorobieff (2006) was numerically investigated. The effects of the Reynolds number,initial condition,intersection angle,length of the wedge edges,and the outer boundary condition were examined. The numerical results showed that the flow in the wedge undergoes a change from symmetrical flow to unsymmetrical flow with a weak backflow,then a vortical (circulation) flow and finally an unsteady jet flow as the Reynolds number is increased for an intersection angle of 32° and a wedge edge of length 30 times the width of the inlet slit. For the unsteady flow,the jet attached to one side of the wedge constantly loses stability and rolls up into a mushroom-shaped vortex-pair near the outlet of the wedge. As the intersection angle is increased to 50°,a stable jet flow is observed as a new regime between the vortex and unsteady regimes. Both the intersection angle and the wedge length have negative effects on the stability of the flow,although the effect of the wedge length on the critical Reynolds number for the symmetry-breaking instability is not pronounced. The outer boundary condition was found not to affect the flow patterns inside the wedge significantly. At a certain Re regime above the onset of symmetry-breaking instability,the flows evolve into steady state very slowly except for the initial stage in the case of decreasing flow flux. Two different solutions can be observed within the normal observation time for the experiment,providing a possible explanation for the hysteresis phenomenon in the experiment.

关键词： Diverging channel Flow structures Bifurcation fictitious domain

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Direct Numerical Simulation of Multiple Particles Sedimentation at an Intermediate Reynolds Number

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Communications in Computational Physics 2014年第8期16卷 675-698页

作者： Deming Nie Jianzhong Lin Mengjiao Zheng Institute of Fluid Mechanics China Jiliang UniversityHangzhou310018China. State Key Laboratory of Fluid Power Transmission and Control Zhejiang UniversityHangzhou 310027China.

In this work the previously developed Lattice Boltzmann-Direct Forcing/fictitious domain(LB-DF/FD)method is adopted to simulate the sedimentation of eight circular particles under gravity at an intermediate Reynolds number of about *** particle clustering and the resulting Drafting-Kissing-Tumbling(DKT)motion which takes place for the first time are *** effects of initial particleparticle gap on the DKT motion are found *** addition,the trajectories of particles are presented under different initial particle-particle gaps,which display totally three kinds of falling patterns provided that no DKT motion takes place,*** concave-down shape,the shape of letter“M”and“in-line”***,the lateral and vertical hydrodynamic forces on the particles are *** has been found that the value of Strouhal number for all particles is the same which is about 0.157 when initial particle-particle gap is relatively *** wall effects on falling patterns and particle expansions are examined in the final.

关键词： Lattice Boltzmann method sedimentation fictitious domain falling pattern

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The Algebraic Immersed Interface and Boundary Method for Elliptic Equations with Jump Conditions

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Open Journal of Fluid Dynamics 2020年第3期10卷 239-269页

作者： Arthur Sarthou Stéphane Vincent Philippe Angot Jean-Paul Caltagirone Buf Compagnie Paris France Laboratoire MSME Université Gustave Eiffel Champs-sur-Marne France Institut de Mathématiques de Marseille Centrale Marseille Marseille France Institut Polytechnique de Bordeaux Université de Bordeaux Talence France

A new simple fictitious domain method, the algebraic immersed interface and boundary (AIIB) method, is presented for elliptic equations with immersed interface conditions. This method allows jump conditions on immersed interfaces to be discretized with a good accuracy on a compact stencil. Auxiliary unknowns are created at existing grid locations to increase the degrees of freedom of the initial problem. These auxiliary unknowns allow imposing various constraints to the system on interfaces of complex shapes. For instance, the method is able to deal with immersed interfaces for elliptic equations with jump conditions on the solution or discontinuous coefficients with a second order of spatial accuracy. As the AIIB method acts on an algebraic level and only changes the problem matrix, no particular attention to the initial discretization is required. The method can be easily implemented in any structured grid code and can deal with immersed boundary problems too. Several validation problems are presented to demonstrate the interest and accuracy of the method.

关键词： fictitious domain Immersed Interface Method Immersed Boundary Method Penalty Methods Finite Volumes Elliptic Equations Jump Embedded Conditions

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