This paper, with a finite element method, studies the interaction of a coupled incompressible fluid-rigid structure system with a free surface subjected to external wave excitations. With this fully coupled model, the...This paper, with a finite element method, studies the interaction of a coupled incompressible fluid-rigid structure system with a free surface subjected to external wave excitations. With this fully coupled model, the rigid structure is taken as ＂fictitious＂ fluid with zero strain rate. Both fluid and structure are described by velocity and pressure. The whole domain, including fluid region and structure region, is modeled by the incompressible Navier-Stokes equations which are discretized with fixed Eulerian mesh. However, to keep the structure＇ s rigid body shape and behavior, a rigid body constraint is enforced on the ＂fictitious＂ fluid domain by use of the Distributed Lagrange Multipher/Fictitious Domain （DLM/ FD） method which is originally introduced to solve particulate flow problems by Glowinski et al. For the verification of the model presented herein, a 2D numerical wave tank is established to simulate small amplitude wave propagations, and then numerical results are compared with analytical solutions. Finally, a 2D example of fluid-structure interaction under wave dynamic forces provides convincing evidences for the method excellent solution quality and fidelity.展开更多
To apply the fictitious domain method and conduct numericalexperiments, a boundary value problem for an ordinary differential equation is considered. The results of numerical calculations for different valuesof the it...To apply the fictitious domain method and conduct numericalexperiments, a boundary value problem for an ordinary differential equation is considered. The results of numerical calculations for different valuesof the iterative parameter τ and the small parameter ε are presented. Astudy of the auxiliary problem of the fictitious domain method for NavierStokes equations with continuation into a fictitious subdomain by highercoefficients with a small parameter is carried out. A generalized solutionof the auxiliary problem of the fictitious domain method with continuationby higher coefficients with a small parameter is determined. After all theabove mathematical studies, a computational algorithm has been developedfor the numerical solution of the problem. Two methods were used to solvethe problem numerically. The first variant is the fictitious domain methodassociated with the modification of nonlinear terms in a fictitious subdomain.The model problem shows the effectiveness of using such a modification. Theproposed version of the method is used to solve two problems at once that arisewhile numerically solving systems of Navier-Stokes equations: the problem ofa curved boundary of an arbitrary domain and the problem of absence of aboundary condition for pressure in physical formulation of the internal flowproblem. The main advantage of this method is its universality in developmentof computer programs. The second method used calculation on a uniform gridinside the area. When numerically implementing the solution on a uniformgrid inside the domain, using this method it’s possible to accurately take intoaccount the boundaries of the curved domain and ensure the accuracy of thevalue of the function at the boundaries of the domain. Methodical calculationswere carried out, the results of numerical calculations were obtained. Whenconducting numerical experiments in both cases, quantitative and qualitativeindicators of numerical results coincide.展开更多
In framework of the fictitious domain methods with immersed interfaces for the elasticity problem,the present contribution is to study and numerically validate the jump-integrated boundary conditions method with sharp...In framework of the fictitious domain methods with immersed interfaces for the elasticity problem,the present contribution is to study and numerically validate the jump-integrated boundary conditions method with sharp interface for the vector elasticity system discretized by a proposed finite volume method.The main idea of the fictitious domain approach consists in embedding the original domain of study into a geometrically larger and simpler one called the fictitious domain.Here,we present a cell-centered finite volume method to discretize the fictitious domain problem.The proposed method is numerically validated for different test cases.This work can be considered as a first step before more challenging problems such as fluid-structure interactions or moving interface problems.展开更多
In this article,we discuss a least-squares/fictitious domain method for the solution of linear elliptic boundary value problems with Robin boundary conditions.LetΩandωbe two bounded domains of R d such thatω⊂Ω.For a...In this article,we discuss a least-squares/fictitious domain method for the solution of linear elliptic boundary value problems with Robin boundary conditions.LetΩandωbe two bounded domains of R d such thatω⊂Ω.For a linear elliptic problem inΩ\ωwith Robin boundary condition on the boundaryγofω,our goal here is to develop a fictitious domain method where one solves a variant of the original problem on the fullΩ,followed by a well-chosen correction overω.This method is of the virtual control type and relies on a least-squares formulation making the problem solvable by a conjugate gradient algorithm operating in a well chosen control space.Numerical results obtained when applying our method to the solution of two-dimensional elliptic and parabolic problems are given;they suggest optimal order of convergence.展开更多
In this paper, we combine the direct-forcing fictitious domain （DF/FD） method and the sharp interface method to resolve the problem of particle dielectrophoresis in two dimensions. The flow field and the motion of p...In this paper, we combine the direct-forcing fictitious domain （DF/FD） method and the sharp interface method to resolve the problem of particle dielectrophoresis in two dimensions. The flow field and the motion of particles are solved with the DF/FD method, the electric field is solved with the sharp inter- face method, and the electrostatic force on the particles is computed using the Maxwell stress tensor method. The proposed method is validated via three problems： effective conductivity of particle compos- ite between two planar plates, cell trapping in a channel, and motion of particles due to both conventional and traveling wave dielectrophoretic forces.展开更多
Experimental observations show that a strong magnetic field has a dramatic influence on the sedimentation of RBCs,which motivates us to model the sedimentation of red blood cell(RBC)under strong external magnetic body...Experimental observations show that a strong magnetic field has a dramatic influence on the sedimentation of RBCs,which motivates us to model the sedimentation of red blood cell(RBC)under strong external magnetic body force.To model the sedimentation of a RBC in a square duct and a circular pipe,a recently developed technique derived from the lattice Boltzmann and the distributed Lagrange multiplier/fictitious domain methods(LBM-DLM/FD)is extended to employ the mesoscopic network model for simulations of the sedimentation of a RBC in flow.The flow is simulated by the LBM with a strong magnetic body force,while the network model is used for modeling RBC deformation.The fluid-RBC interactions are enforced by the Lagrange multiplier.The sedimentation of RBC in a square duct and a circular pipe is simulated,which demonstrates the developed method’s capability to model the sedimentation of RBCs in various flows.Numerical results illustrate that the terminal settling velocity increases incrementally with the exerted body force.The deformation of RBC has a significant effect on the terminal settling velocity due to the change in the frontal area.The larger the exerted force,the smaller the frontal area and the larger the RBC deformation become.Additionally,the wall effect on the motion and deformation of RBC is also investigated.展开更多
The sedimentation of a single circular particle between two parallel walls was studied by means of direct numerical simulation (DNS) and experiment. The improved implementation of distributed Lagrange multiplier/ficti...The sedimentation of a single circular particle between two parallel walls was studied by means of direct numerical simulation (DNS) and experiment. The improved implementation of distributed Lagrange multiplier/fictitious domain method used in our DNS is a promising new way for simulation of particulate flows. The settling behaviors of the particle are presented ranging in Reynolds number from 0 to about 700, which showed that our results for low Reynolds numbers agreed well with that reported before. Nevertheless, for higher Reynolds numbers our results were different from theirs. The long-term mean equilibrium positions in our results were all on the centerline, but not at off-center position as reported before. In order to validate our simulation, experiments were also conducted. The results showed that the sedimenting behavior simulated in this paper agreed well with our experiment result.展开更多
We present the simulation of the dynamics of fluid-cylinder interactions in a narrow three-dimensional channel filled with a Newtonian fluid, using a Lagrange multiplier based fictitious domain methodology combined wi...We present the simulation of the dynamics of fluid-cylinder interactions in a narrow three-dimensional channel filled with a Newtonian fluid, using a Lagrange multiplier based fictitious domain methodology combined with a finite element method and an operator splitting technique. As expected, a settling truncated cylinder turns its broadside perpendicular to the main stream direction and the center of mass moves to the central axis of the channel. In the case of two truncated cylinders, they first move around each other for a while and then stay together in a "T" shape. After the "T" shape has been formed for a long enough time, we found no vortex shedding behind the cylinders. When simulating the fluidization of 60 truncated cylinders, we captured the features of interactions among fluidized cylinders as observed in experiments.展开更多
An improved implementation of Distributed Lagrange multiplier/fictitious domain method was presented and used to simulate the interactions between two circular particles sedimenting in a two_dimensional channel. The s...An improved implementation of Distributed Lagrange multiplier/fictitious domain method was presented and used to simulate the interactions between two circular particles sedimenting in a two_dimensional channel. The simulation results were verified by comparison with experiments. The results show that the interactions between two particles with different sizes can be described as drafting, kissing, tumbling and separating. Only for small diameter ratio, the two particles will interact undergoing repeated DKT (Drafting, Kissing and Tumbling) process. Otherwise, the two particles will separate after their tumbling. The results also show that, during the interaction process, the motion of the small particle is strongly affected while the large particle is affected slightly.展开更多
An improved implementation of distributed multiplier/fictitious domain method is presented for the direct numerical simulation of particulate flow. The key improvement is to replace a finite element triangulation for...An improved implementation of distributed multiplier/fictitious domain method is presented for the direct numerical simulation of particulate flow. The key improvement is to replace a finite element triangulation for the velocity and a “twice coarser' triangulation for the pressure with a rectangular discretization for the velocity and pressure. For code validation, the sedimentation of a single particle in a two dimensional channel was simulated. The results showed that the simulation is independent of the mesh size as well as the time step. The comparison between experimental data and this simulation showed that our code can give a more accurate simulation on the motion of particles than previous DLM code. The code was then applied to simulate the sedimentation of 600 particles in a rectangular box. The falling course is presented and discussed. At the same time, this simulation also demonstrates that the method presented in this paper can be used for solving the initial problems involving a lager number of particles exactly with computing durations kept at acceptable levels.展开更多
A parallelized resolved method for the simulation of the dynamics of immersed bodies within fluids is presented. The algorithm uses a FDM （fictitious domain method） and combines the Lagrangian DEM （discrete element...A parallelized resolved method for the simulation of the dynamics of immersed bodies within fluids is presented. The algorithm uses a FDM （fictitious domain method） and combines the Lagrangian DEM （discrete element method） for tracking the bodies with a CFD （computational fluid dynamics） method for calculating the dynamics of the fluid phase. First the CFD-calculation is carried out, disregarding the solid bodies. Afterwards, the velocity information from the bodies is included and the force, the fluid imposes onto the bodies, is computed. The last step consists of a correction-operation which ensures the fulfillment of the conservation equation. Dynamic local mesh refinement is used for minimizing the number of fluid cells. The CFD-DEM coupling is realized within the Open Source framework CFDEMcoupling （www.cfdem.com）, where the DEM software LIGGGHTS （www.liggghts.com） is linked against an OpenFOAM^-based CFD solver. While both LIGGGHTS and the CFD solver were already parallelized, only a recent improvement of the algorithm permits the fully parallel computation of resolved problems. This parallelization permits the treatment of large-scale problems. The enclosed validation and application examples show the dynamics of the flow around settling and rotating spheres as well as an investigation of the settling of spheres regarding the Boycott effect.展开更多
A spring model is used to simulate the skeleton structure of the red blood cell (RBC) membrane and to study the red blood cell (RBC) rheology in Poiseuille flow with an immersed boundary method. The lateral migration ...A spring model is used to simulate the skeleton structure of the red blood cell (RBC) membrane and to study the red blood cell (RBC) rheology in Poiseuille flow with an immersed boundary method. The lateral migration properties of many cells in Poiseuille flow have been investigated. The authors also combine the above methodology with a distributed Lagrange multiplier/fictitious domain method to simulate the interaction of cells and neutrally buoyant particles in a microchannel for studying the margination of particles.展开更多
In this paper, we propose a lattice Boltzmann (LB) method coupled with adirect-forcing fictitious domain (DF/FD) method for the simulation of particle suspensions. This method combines the good features of the LB and ...In this paper, we propose a lattice Boltzmann (LB) method coupled with adirect-forcing fictitious domain (DF/FD) method for the simulation of particle suspensions. This method combines the good features of the LB and the DF/FD methodsby using two unrelated meshes, namely, an Eulerian mesh for the flow domain and aLagrangian mesh for the solid domain, which avoids the re-meshing procedure anddoes not need to calculate the hydrodynamic forces at each time step. The non-slipboundary condition is enforced by introducing a forcing term into the lattice Boltzmann equation, which preserves all remarkable advantages of the LBM in simulatingfluid flows. The present LB-DF/FD method has been validated by comparing its results with analytical results and previous numerical results for a single circular particleand two circular particles settling under gravity. The interaction between particle andwall, the process of drafting-kissing-tumbling (DKT) of two settling particles will bedemonstrated. As a manifestation of the efficiency of the present method, the settlingof a large number (128) of circular particles is simulated in an enclosure.展开更多
.In this paper,an augmented Lagrangian Uzawa iterative method is developed and analyzed for solving a class of double saddle-point systems with semidefinite(2,2)block.Convergence of the iterativemethod is proved under....In this paper,an augmented Lagrangian Uzawa iterative method is developed and analyzed for solving a class of double saddle-point systems with semidefinite(2,2)block.Convergence of the iterativemethod is proved under the assumption that the double saddle-point problem exists a unique solution.An application of the iterative method to the double saddle-point systems arising from the distributed Lagrange multiplier/fictitious domain(DLM/FD)finite element method for solving elliptic interface problems is also presented,in which the existence and uniqueness of the double saddle-point system is guaranteed by the analysis of the DLM/FD finite element method.Numerical experiments are conducted to validate the theoretical results and to study the performance of the proposed iterative method.展开更多
In this paper, a new method-Distributed La-grange Multiplier/fictitiousdomain (DLM) method for partic-ulate flows was improved. A rectangular mesh was introduced todiscretize the domain, and the buoyant force was cons...In this paper, a new method-Distributed La-grange Multiplier/fictitiousdomain (DLM) method for partic-ulate flows was improved. A rectangular mesh was introduced todiscretize the domain, and the buoyant force was considered for predicting the positions ofparticles. In order to validate the presented algorithm, the sedimentation of a single circularparticle was simulated using different mesh sizes and time steps firstly. The results show that thesimulation is independent of the mesh size as well as the time step. And then, the interactionsbetween two falling particles, including drafting, kissing and tumbling, and the sedimentation of 18particles also have been simulated with the code.展开更多
The direct-forcing fictitious domain method is extended to simulate the locomotion of a passively pitching foil. Our study focuses on the hysteresis phenomenon that the critical frequency for the reverse of the locomo...The direct-forcing fictitious domain method is extended to simulate the locomotion of a passively pitching foil. Our study focuses on the hysteresis phenomenon that the critical frequency for the reverse of the locomotion direction of the wing in case of decreasing frequency is smaller than that in case of increasing frequency. In our simulations, the hysteresis phenomenon is produced by imposing different initial conditions at a same frequency. Our results indicate that the ratio of the heaving amplitudes of two foil edges is crucial to the direction of the foil＇s horizontal motion, and the amplitude of the leading edge is generally smaller. The critical frequencies for the reverse of the locomotion direction are increased, when the foil-fluid density ratio is decreased or the spring constant is increased. The critical frequencies in the bi-stability regime also depend on the initial velocity imposed, and the hysteresis loop generally becomes larger if the initial velocities are closer to the terminal locomotion velocities of the foil.展开更多
The hemodynamic interactions of red blood cells （RBCs） in a microcapillary flow are investigated in this paper. This kind of interaction is considered as the non-contact mutual interaction of cells, which is importa...The hemodynamic interactions of red blood cells （RBCs） in a microcapillary flow are investigated in this paper. This kind of interaction is considered as the non-contact mutual interaction of cells, which is important in the suspension flow of blood, but not sufficiently understood. The distributed Lagrange multiplier/fictitious domain method in the lattice Boltzmann framework is used to solve the suspension of the RBCs. The modification of the flow due to the cells, the dependence of the cell deformation on the flow and the cell-cell interaction via the fluid are discussed. It is revealed that the long-range hydrodynamic interaction with a long interacting distance, more than about 5 times of the RBC equivalent radius, mainly has effect on the rheology properties of the suspension, such as the mean velocity, and the short-range interaction is sensitive to the shape of the cell in the microcapillary flow. The flow velocity around the cell plays a key role in the cell deformation. In the current configuration of the flow and cells, the cells repel each other along the capillary.展开更多
A parallel direct-forcing fictitious domain method is applied in fully-resolved numerical simulations of particle-laden turbulent flows in a square duct. The effects of finite-size heavy particles on the mean secondar...A parallel direct-forcing fictitious domain method is applied in fully-resolved numerical simulations of particle-laden turbulent flows in a square duct. The effects of finite-size heavy particles on the mean secondary flow, the mean streamwise velocity, the root-meansquare velocity fluctuation, and the particle concentration distribution are investigated at the friction Reynolds number of 150, the particle volume fraction of 2.36%, the particle diameter of 0.1 duct width, and the Shields number ranging from 1.0 to 0.2 Our results show that the particle sedimentation breaks the up-down symmetry of the mean secondary vortices, and results in a stronger secondary-flow circulation which transports the fluids downward in the bulk center region and upward along the side walls at a low Shields number. This circulation has a significant impact on the distribution of the mean streamwise velocity, whose maximum value occurs in the lower half duct, unlike in the plane channel case. The flow resistance is increased and the turbulence intensity is reduced, as the Shields number is decreased. The particles accumulate preferentially at the face center of the bottom wall, due to the effect of the mean secondary flow. It is observed that the collision model has an important effect on the results, but does not change the results qualitatively.展开更多
The paper concerns an analysis of equilibrium problems for 2D elastic bodies with a thin Timoshenko inclusion crossing an external boundary at zero angle. The inclusion is assumed to be delaminated, thus forming a cra...The paper concerns an analysis of equilibrium problems for 2D elastic bodies with a thin Timoshenko inclusion crossing an external boundary at zero angle. The inclusion is assumed to be delaminated, thus forming a crack between the inclusion and the body. We consider elastic inclusions as well as rigid inclusions. To prevent a mutual penetration between the crack faces, inequality type boundary conditions are imposed at the crack faces. Theorems of existence and uniqueness are established. Passages to limits are investigated as a rigidity parameter of the elastic inclusion going to infinity.展开更多
Distributed Lagrange Multiplier/Fictitious Domain （DLM/FD） method was employed to simulate the channel flow with polymer suspension. The polymer molecules were modeled as Finitely Extensible Nonlinear Elastic （FENE...Distributed Lagrange Multiplier/Fictitious Domain （DLM/FD） method was employed to simulate the channel flow with polymer suspension. The polymer molecules were modeled as Finitely Extensible Nonlinear Elastic （FENE） chains and FENE chain cluster. The coiled stretched transition of FENE chains was examined and the change in configuration of FENE chains was presented. The average velocity profile of the fully developed channel flow with 64 FENE chains was given and fitted well with the power-law curve. The change of chain cluster configuration was also simulated. These simulations show that DLM/FD method is capable of simulating the motion of not only FENE chain, but also FENE chain cluster.展开更多
基金This study is supported by the National Natural Science Foundation of China (Grant No50579046) the Science Foundation of Tianjin Municipal Commission of Science and Technology (Grant No043114711)
文摘This paper, with a finite element method, studies the interaction of a coupled incompressible fluid-rigid structure system with a free surface subjected to external wave excitations. With this fully coupled model, the rigid structure is taken as ＂fictitious＂ fluid with zero strain rate. Both fluid and structure are described by velocity and pressure. The whole domain, including fluid region and structure region, is modeled by the incompressible Navier-Stokes equations which are discretized with fixed Eulerian mesh. However, to keep the structure＇ s rigid body shape and behavior, a rigid body constraint is enforced on the ＂fictitious＂ fluid domain by use of the Distributed Lagrange Multipher/Fictitious Domain （DLM/ FD） method which is originally introduced to solve particulate flow problems by Glowinski et al. For the verification of the model presented herein, a 2D numerical wave tank is established to simulate small amplitude wave propagations, and then numerical results are compared with analytical solutions. Finally, a 2D example of fluid-structure interaction under wave dynamic forces provides convincing evidences for the method excellent solution quality and fidelity.
基金This research is funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan(Grant No.AP09058430)。
文摘To apply the fictitious domain method and conduct numericalexperiments, a boundary value problem for an ordinary differential equation is considered. The results of numerical calculations for different valuesof the iterative parameter τ and the small parameter ε are presented. Astudy of the auxiliary problem of the fictitious domain method for NavierStokes equations with continuation into a fictitious subdomain by highercoefficients with a small parameter is carried out. A generalized solutionof the auxiliary problem of the fictitious domain method with continuationby higher coefficients with a small parameter is determined. After all theabove mathematical studies, a computational algorithm has been developedfor the numerical solution of the problem. Two methods were used to solvethe problem numerically. The first variant is the fictitious domain methodassociated with the modification of nonlinear terms in a fictitious subdomain.The model problem shows the effectiveness of using such a modification. Theproposed version of the method is used to solve two problems at once that arisewhile numerically solving systems of Navier-Stokes equations: the problem ofa curved boundary of an arbitrary domain and the problem of absence of aboundary condition for pressure in physical formulation of the internal flowproblem. The main advantage of this method is its universality in developmentof computer programs. The second method used calculation on a uniform gridinside the area. When numerically implementing the solution on a uniformgrid inside the domain, using this method it’s possible to accurately take intoaccount the boundaries of the curved domain and ensure the accuracy of thevalue of the function at the boundaries of the domain. Methodical calculationswere carried out, the results of numerical calculations were obtained. Whenconducting numerical experiments in both cases, quantitative and qualitativeindicators of numerical results coincide.
文摘In framework of the fictitious domain methods with immersed interfaces for the elasticity problem,the present contribution is to study and numerically validate the jump-integrated boundary conditions method with sharp interface for the vector elasticity system discretized by a proposed finite volume method.The main idea of the fictitious domain approach consists in embedding the original domain of study into a geometrically larger and simpler one called the fictitious domain.Here,we present a cell-centered finite volume method to discretize the fictitious domain problem.The proposed method is numerically validated for different test cases.This work can be considered as a first step before more challenging problems such as fluid-structure interactions or moving interface problems.
基金The first author acknowledge the support of the Institute for Advanced Study(IAS)at The Hong Kong University of Science and TechnologyThe work is partially supported by grants from RGC CA05/06.SC01 and RGC-CERG 603107.
文摘In this article,we discuss a least-squares/fictitious domain method for the solution of linear elliptic boundary value problems with Robin boundary conditions.LetΩandωbe two bounded domains of R d such thatω⊂Ω.For a linear elliptic problem inΩ\ωwith Robin boundary condition on the boundaryγofω,our goal here is to develop a fictitious domain method where one solves a variant of the original problem on the fullΩ,followed by a well-chosen correction overω.This method is of the virtual control type and relies on a least-squares formulation making the problem solvable by a conjugate gradient algorithm operating in a well chosen control space.Numerical results obtained when applying our method to the solution of two-dimensional elliptic and parabolic problems are given;they suggest optimal order of convergence.
基金support from the National Natural Science Foundation of China(no.10872181)the National Basic Research Program of China(no.2006CB705400)+1 种基金Chinese Universities Scientific Fundthe Major Program of the National Natural Science Foundation of China(no.10632070)
文摘In this paper, we combine the direct-forcing fictitious domain （DF/FD） method and the sharp interface method to resolve the problem of particle dielectrophoresis in two dimensions. The flow field and the motion of particles are solved with the DF/FD method, the electric field is solved with the sharp inter- face method, and the electrostatic force on the particles is computed using the Maxwell stress tensor method. The proposed method is validated via three problems： effective conductivity of particle compos- ite between two planar plates, cell trapping in a channel, and motion of particles due to both conventional and traveling wave dielectrophoretic forces.
基金support from the National Natural Science Foundation of China(Grant Nos.10902098,11372278)the Fundamental Research Funds of the Central Universities(Program No.2010QNA40107)support from the Applied Mathematics Program within the Department of Energys(DOE)Office of Advanced Scientific Computing Research(ASCR)as part of the Collaboratory on Mathematics for Mesoscopic Modeling of Materials(CM4)。
文摘Experimental observations show that a strong magnetic field has a dramatic influence on the sedimentation of RBCs,which motivates us to model the sedimentation of red blood cell(RBC)under strong external magnetic body force.To model the sedimentation of a RBC in a square duct and a circular pipe,a recently developed technique derived from the lattice Boltzmann and the distributed Lagrange multiplier/fictitious domain methods(LBM-DLM/FD)is extended to employ the mesoscopic network model for simulations of the sedimentation of a RBC in flow.The flow is simulated by the LBM with a strong magnetic body force,while the network model is used for modeling RBC deformation.The fluid-RBC interactions are enforced by the Lagrange multiplier.The sedimentation of RBC in a square duct and a circular pipe is simulated,which demonstrates the developed method’s capability to model the sedimentation of RBCs in various flows.Numerical results illustrate that the terminal settling velocity increases incrementally with the exerted body force.The deformation of RBC has a significant effect on the terminal settling velocity due to the change in the frontal area.The larger the exerted force,the smaller the frontal area and the larger the RBC deformation become.Additionally,the wall effect on the motion and deformation of RBC is also investigated.
文摘The sedimentation of a single circular particle between two parallel walls was studied by means of direct numerical simulation (DNS) and experiment. The improved implementation of distributed Lagrange multiplier/fictitious domain method used in our DNS is a promising new way for simulation of particulate flows. The settling behaviors of the particle are presented ranging in Reynolds number from 0 to about 700, which showed that our results for low Reynolds numbers agreed well with that reported before. Nevertheless, for higher Reynolds numbers our results were different from theirs. The long-term mean equilibrium positions in our results were all on the centerline, but not at off-center position as reported before. In order to validate our simulation, experiments were also conducted. The results showed that the sedimenting behavior simulated in this paper agreed well with our experiment result.
文摘We present the simulation of the dynamics of fluid-cylinder interactions in a narrow three-dimensional channel filled with a Newtonian fluid, using a Lagrange multiplier based fictitious domain methodology combined with a finite element method and an operator splitting technique. As expected, a settling truncated cylinder turns its broadside perpendicular to the main stream direction and the center of mass moves to the central axis of the channel. In the case of two truncated cylinders, they first move around each other for a while and then stay together in a "T" shape. After the "T" shape has been formed for a long enough time, we found no vortex shedding behind the cylinders. When simulating the fluidization of 60 truncated cylinders, we captured the features of interactions among fluidized cylinders as observed in experiments.
文摘An improved implementation of Distributed Lagrange multiplier/fictitious domain method was presented and used to simulate the interactions between two circular particles sedimenting in a two_dimensional channel. The simulation results were verified by comparison with experiments. The results show that the interactions between two particles with different sizes can be described as drafting, kissing, tumbling and separating. Only for small diameter ratio, the two particles will interact undergoing repeated DKT (Drafting, Kissing and Tumbling) process. Otherwise, the two particles will separate after their tumbling. The results also show that, during the interaction process, the motion of the small particle is strongly affected while the large particle is affected slightly.
基金TheNationalNaturalSciencesFoundationforOutstandingYouthofChina (No .19925210)andZhejiangProvincialNaturalScienceFoundationofChina(No .10 10 4 7)
文摘An improved implementation of distributed multiplier/fictitious domain method is presented for the direct numerical simulation of particulate flow. The key improvement is to replace a finite element triangulation for the velocity and a “twice coarser' triangulation for the pressure with a rectangular discretization for the velocity and pressure. For code validation, the sedimentation of a single particle in a two dimensional channel was simulated. The results showed that the simulation is independent of the mesh size as well as the time step. The comparison between experimental data and this simulation showed that our code can give a more accurate simulation on the motion of particles than previous DLM code. The code was then applied to simulate the sedimentation of 600 particles in a rectangular box. The falling course is presented and discussed. At the same time, this simulation also demonstrates that the method presented in this paper can be used for solving the initial problems involving a lager number of particles exactly with computing durations kept at acceptable levels.
文摘A parallelized resolved method for the simulation of the dynamics of immersed bodies within fluids is presented. The algorithm uses a FDM （fictitious domain method） and combines the Lagrangian DEM （discrete element method） for tracking the bodies with a CFD （computational fluid dynamics） method for calculating the dynamics of the fluid phase. First the CFD-calculation is carried out, disregarding the solid bodies. Afterwards, the velocity information from the bodies is included and the force, the fluid imposes onto the bodies, is computed. The last step consists of a correction-operation which ensures the fulfillment of the conservation equation. Dynamic local mesh refinement is used for minimizing the number of fluid cells. The CFD-DEM coupling is realized within the Open Source framework CFDEMcoupling （www.cfdem.com）, where the DEM software LIGGGHTS （www.liggghts.com） is linked against an OpenFOAM^-based CFD solver. While both LIGGGHTS and the CFD solver were already parallelized, only a recent improvement of the algorithm permits the fully parallel computation of resolved problems. This parallelization permits the treatment of large-scale problems. The enclosed validation and application examples show the dynamics of the flow around settling and rotating spheres as well as an investigation of the settling of spheres regarding the Boycott effect.
基金supported by the National Science Foundation of the United States (Nos. ECS-9527123, CTS-9873236, DMS-9973318, CCR-9902035, DMS-0209066, DMS-0443826, DMS-0914788)
文摘A spring model is used to simulate the skeleton structure of the red blood cell (RBC) membrane and to study the red blood cell (RBC) rheology in Poiseuille flow with an immersed boundary method. The lateral migration properties of many cells in Poiseuille flow have been investigated. The authors also combine the above methodology with a distributed Lagrange multiplier/fictitious domain method to simulate the interaction of cells and neutrally buoyant particles in a microchannel for studying the margination of particles.
基金This work was supported by the Scientific Project of Zhejiang Province of China(No.2008C01024-4).
文摘In this paper, we propose a lattice Boltzmann (LB) method coupled with adirect-forcing fictitious domain (DF/FD) method for the simulation of particle suspensions. This method combines the good features of the LB and the DF/FD methodsby using two unrelated meshes, namely, an Eulerian mesh for the flow domain and aLagrangian mesh for the solid domain, which avoids the re-meshing procedure anddoes not need to calculate the hydrodynamic forces at each time step. The non-slipboundary condition is enforced by introducing a forcing term into the lattice Boltzmann equation, which preserves all remarkable advantages of the LBM in simulatingfluid flows. The present LB-DF/FD method has been validated by comparing its results with analytical results and previous numerical results for a single circular particleand two circular particles settling under gravity. The interaction between particle andwall, the process of drafting-kissing-tumbling (DKT) of two settling particles will bedemonstrated. As a manifestation of the efficiency of the present method, the settlingof a large number (128) of circular particles is simulated in an enclosure.
基金supported by the 10 plus 10 project of Tongji University(No.4260141304/004/010).
文摘.In this paper,an augmented Lagrangian Uzawa iterative method is developed and analyzed for solving a class of double saddle-point systems with semidefinite(2,2)block.Convergence of the iterativemethod is proved under the assumption that the double saddle-point problem exists a unique solution.An application of the iterative method to the double saddle-point systems arising from the distributed Lagrange multiplier/fictitious domain(DLM/FD)finite element method for solving elliptic interface problems is also presented,in which the existence and uniqueness of the double saddle-point system is guaranteed by the analysis of the DLM/FD finite element method.Numerical experiments are conducted to validate the theoretical results and to study the performance of the proposed iterative method.
文摘In this paper, a new method-Distributed La-grange Multiplier/fictitiousdomain (DLM) method for partic-ulate flows was improved. A rectangular mesh was introduced todiscretize the domain, and the buoyant force was considered for predicting the positions ofparticles. In order to validate the presented algorithm, the sedimentation of a single circularparticle was simulated using different mesh sizes and time steps firstly. The results show that thesimulation is independent of the mesh size as well as the time step. And then, the interactionsbetween two falling particles, including drafting, kissing and tumbling, and the sedimentation of 18particles also have been simulated with the code.
基金Project supported by the National Natural Science Foun-dation of China(Grant No.11372275)the Program for New Century Excellent Talents in University
文摘The direct-forcing fictitious domain method is extended to simulate the locomotion of a passively pitching foil. Our study focuses on the hysteresis phenomenon that the critical frequency for the reverse of the locomotion direction of the wing in case of decreasing frequency is smaller than that in case of increasing frequency. In our simulations, the hysteresis phenomenon is produced by imposing different initial conditions at a same frequency. Our results indicate that the ratio of the heaving amplitudes of two foil edges is crucial to the direction of the foil＇s horizontal motion, and the amplitude of the leading edge is generally smaller. The critical frequencies for the reverse of the locomotion direction are increased, when the foil-fluid density ratio is decreased or the spring constant is increased. The critical frequencies in the bi-stability regime also depend on the initial velocity imposed, and the hysteresis loop generally becomes larger if the initial velocities are closer to the terminal locomotion velocities of the foil.
基金supported by the National Natural Science Foundation of China(Grant Nos.11372278,10902098)the Fundamental Research Funds of the Central Universities(Grant No.2010QNA40107)
文摘The hemodynamic interactions of red blood cells （RBCs） in a microcapillary flow are investigated in this paper. This kind of interaction is considered as the non-contact mutual interaction of cells, which is important in the suspension flow of blood, but not sufficiently understood. The distributed Lagrange multiplier/fictitious domain method in the lattice Boltzmann framework is used to solve the suspension of the RBCs. The modification of the flow due to the cells, the dependence of the cell deformation on the flow and the cell-cell interaction via the fluid are discussed. It is revealed that the long-range hydrodynamic interaction with a long interacting distance, more than about 5 times of the RBC equivalent radius, mainly has effect on the rheology properties of the suspension, such as the mean velocity, and the short-range interaction is sensitive to the shape of the cell in the microcapillary flow. The flow velocity around the cell plays a key role in the cell deformation. In the current configuration of the flow and cells, the cells repel each other along the capillary.
基金Project supported by the National Natural Science Foun-dation of China(Grant Nos.11372275,51376162)the Resea-rch Fund for the Doctoral Program of Higher Education of China(Grant No.20130101110035)
文摘A parallel direct-forcing fictitious domain method is applied in fully-resolved numerical simulations of particle-laden turbulent flows in a square duct. The effects of finite-size heavy particles on the mean secondary flow, the mean streamwise velocity, the root-meansquare velocity fluctuation, and the particle concentration distribution are investigated at the friction Reynolds number of 150, the particle volume fraction of 2.36%, the particle diameter of 0.1 duct width, and the Shields number ranging from 1.0 to 0.2 Our results show that the particle sedimentation breaks the up-down symmetry of the mean secondary vortices, and results in a stronger secondary-flow circulation which transports the fluids downward in the bulk center region and upward along the side walls at a low Shields number. This circulation has a significant impact on the distribution of the mean streamwise velocity, whose maximum value occurs in the lower half duct, unlike in the plane channel case. The flow resistance is increased and the turbulence intensity is reduced, as the Shields number is decreased. The particles accumulate preferentially at the face center of the bottom wall, due to the effect of the mean secondary flow. It is observed that the collision model has an important effect on the results, but does not change the results qualitatively.
文摘The paper concerns an analysis of equilibrium problems for 2D elastic bodies with a thin Timoshenko inclusion crossing an external boundary at zero angle. The inclusion is assumed to be delaminated, thus forming a crack between the inclusion and the body. We consider elastic inclusions as well as rigid inclusions. To prevent a mutual penetration between the crack faces, inequality type boundary conditions are imposed at the crack faces. Theorems of existence and uniqueness are established. Passages to limits are investigated as a rigidity parameter of the elastic inclusion going to infinity.
文摘Distributed Lagrange Multiplier/Fictitious Domain （DLM/FD） method was employed to simulate the channel flow with polymer suspension. The polymer molecules were modeled as Finitely Extensible Nonlinear Elastic （FENE） chains and FENE chain cluster. The coiled stretched transition of FENE chains was examined and the change in configuration of FENE chains was presented. The average velocity profile of the fully developed channel flow with 64 FENE chains was given and fitted well with the power-law curve. The change of chain cluster configuration was also simulated. These simulations show that DLM/FD method is capable of simulating the motion of not only FENE chain, but also FENE chain cluster.
