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Particulate Flow Simulation via a Boundary condition-Enforced Immersed Boundary-Lattice Boltzmann Scheme

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communications in computational Physics 2010年第4期7卷 793-812页

作者： J.Wu c.shu Department of Mechanical Engineering National University of Singapore10 Kent Ridge CrescentSingapore 119260

A boundary condition-enforced immersed boundary-lattice Boltzmannmethod (IB-LBM) for the simulation of particulate flows is presented in this paper. Ingeneral, the immersed boundary method (IBM) utilizes a discrete set of force densityto represent the effect of boundary. In the conventional IB-LBM, such force density ispre-determined, which cannot guarantee exact satisfaction of non-slip boundary condition. In this study, the force density is transferred to the unknown velocity correctionwhich is determined by enforcing the non-slip boundary condition. For the particulateflows, accurate calculation of hydrodynamic force exerted on the boundary of particlesis of great importance as it controls the motion of particles. The capability of presentmethod for particulate flows is depicted by simulating migration of one particle in asimple shear flow and sedimentation of one particle in a box and two particles in achannel. The expected phenomena and numerical results are achieved. In addition,particle suspension in a 2D symmetric stenotic artery is also simulated.

关键词： Lattice Boltzmann method immersed boundary method non-slip boundary condition particulate flow two-dimensional

Simulation of Incompressible Viscous Flows by Local DFD-Immersed Boundary Method

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Advances in Applied Mathematics and Mechanics 2012年第3期4卷 311-324页

作者： Y.L.Wu c.shu H.Ding Department of Mechanical Engineering National University of Singapore10 Kent Ridge CrescentSingapore 117576 Department of Modern Mechanics University of Science and Technology of ChinaHefeiAnhui 230026China

A local domain-free discretization-immersed boundary method(DFDIBM)is presented in this paper to solve incompressible Navier-Stokes equations in the primitive variable form.Like the conventional immersed boundary method(IBM),the local DFD-IBM solves the governing equations in the whole domain including exterior and interior of the immersed object.The effect of immersed boundary to the surrounding fluids is through the evaluation of velocity at interior and exterior dependent points.To be specific,the velocity at interior dependent points is computed by approximate forms of solution and the velocity at exterior dependent points is set to the wall velocity.As compared to the conventional IBM,the present approach accurately implements the non-slip boundary condition.As a result,there is no flow penetration,which is often appeared in the conventional IBM results.The present approach is validated by its application to simulate incompressible viscous flows around a circular cylinder.The obtained numerical results agree very well with the data in the literature.

关键词： Local domain free discretization(local DFD) immersed boundary method(IBM) incompressible flow flow past a circular cylinder

Three-Dimensional Lattice Kinetic Scheme and its Application to Simulate Incompressible Viscous Thermal Flows

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communications in computational Physics 2007年第2期2卷 239-254页

作者： Y.Peng c.shu Y.T.chew Department of Mechanical Engineering National University of Singapore10 Kent Ridge CrescentSingapore 119260.

In this paper,the three-dimensional lattice kinetic scheme is presented to simulate incompressible viscous thermal flows.As compared with the standard LBM,the present scheme has the following good features.It can save the computer memory since there is no need to store the density distributions.Like the conventional NS solvers,the implementation of boundary conditions is straightforward since the dependent variables are the macroscopic flow parameters.The easy implementation of boundary conditions is a good property for solving three-dimensional flow problems.The present scheme is validated by simulating the three-dimensional natural convection in an air-filled cubical enclosure,which is heated differentially at two vertical side walls.The obtained numerical results compare very well with available data in the literature.

关键词： Lattice kinetic scheme lattice Boltzmann method three-dimensional incompressible flow natural convection thermal flow.

Development and comparative Studies of Three Non-free Parameter Lattice Boltzmann Models for Simulation of compressible Flows

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Advances in Applied Mathematics and Mechanics 2012年第4期4卷 454-472页

作者： L.M.Yang c.shu J.Wu Department of Aerodynamics College of Aerospace EngineeringNanjing University of Aeronautics and AstronauticsYudao StreetNanjing 210016JiangsuChina Department of Mechanical Engineering National University of Singapore10 Kent Ridge CrescentSingapore 119260Singapore

This paper at first shows the details of finite volume-based lattice Boltzmann method(FV-LBM)for simulation of compressible flows with shock waves.In the FV-LBM,the normal convective flux at the interface of a cell is evaluated by using one-dimensional compressible lattice Boltzmann model,while the tangential flux is calculated using the same way as used in the conventional Euler solvers.The paper then presents a platform to construct one-dimensional compressible lattice Boltzmann model for its use in FV-LBM.The platform is formed from the conservation forms of moments.Under the platform,both the equilibrium distribution functions and lattice velocities can be determined,and therefore,non-free parameter model can be developed.The paper particularly presents three typical non-free parameter models,D1Q3,D1Q4 and D1Q5.The performances of these three models for simulation of compressible flows are investigated by a brief analysis and their application to solve some one-dimensional and two-dimensional test problems.Numerical results showed that D1Q3 model costs the least computation time and D1Q4 and D1Q5 models have the wider application range of Mach number.From the results,it seems that D1Q4 model could be the best choice for the FVLBM simulation of hypersonic flows.

关键词： FV-LBM non-free parameter models compressible inviscid flows

A Hybrid Lattice Boltzmann Flux Solver for Simulation of Viscous compressible Flows

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Advances in Applied Mathematics and Mechanics 2016年第6期8卷 887-910页

作者： L.M.Yang c.shu J.Wu State Key Laboratory of Aerodynamics China Aerodynamics Research and Development CenterMianyang 621000China Department of Aerodynamics College of Aerospace EngineeringNanjing University of Aeronautics and AstronauticsYudao StreetNanjing 210016China Department of Mechanical Engineering National University of Singapore10 Kent Ridge CrescentSingapore 119260Singapore

In this paper,a hybrid lattice Boltzmann flux solver(LBFS)is proposed for simulation of viscous compressible flows.In the solver,the finite volume method is applied to solve the Navier-Stokes equations.Different from conventional Navier-Stokes solvers,in this work,the inviscid flux across the cell interface is evaluated by local reconstruction of solution using one-dimensional lattice Boltzmann model,while the viscous flux is still approximated by conventional smooth function approximation.The present work overcomes the two major drawbacks of existing LBFS[28–31],which is used for simulation of inviscid flows.The first one is its ability to simulate viscous flows by including evaluation of viscous flux.The second one is its ability to effectively capture both strong shock waves and thin boundary layers through introduction of a switch function for evaluation of inviscid flux,which takes a value close to zero in the boundary layer and one around the strong shock wave.Numerical experiments demonstrate that the present solver can accurately and effectively simulate hypersonic viscous flows.

关键词： Lattice Boltzmann flux solver hybrid 1D lattice Boltzmann model switch function

Development of Lattice Boltzmann Flux Solver for Simulation of Incompressible Flows

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Advances in Applied Mathematics and Mechanics 2014年第4期6卷 436-460页

作者： c.shu Y.Wang c.J.Teo J.Wu Department of Mechanical Engineering National University of Singapore10 Kent Ridge CrescentSingapore 119260 Department of Aerodynamics College of Aerospace EngineeringNanjing University of Aeronautics and AstronauticsNanjing 210016China

A lattice Boltzmann flux solver(LBFS)is presented in this work for simulation of incompressible viscous and inviscid flows.The new solver is based on chapman-Enskog expansion analysis,which is the bridge to link Navier-Stokes(N-S)equations and lattice Boltzmann equation(LBE).The macroscopic differential equations are discretized by the finite volume method,where the flux at the cell interface is evaluated by local reconstruction of lattice Boltzmann solution from macroscopic flow variables at cell centers.The new solver removes the drawbacks of conventional lattice Boltzmann method such as limitation to uniform mesh,tie-up of mesh spacing and time interval,limitation to viscous flows.LBFS is validated by its application to simulate the viscous decaying vortex flow,the driven cavity flow,the viscous flow past a circular cylinder,and the inviscid flow past a circular cylinder.The obtained numerical results compare very well with available data in the literature,which show that LBFS has the second order of accuracy in space,and can be well applied to viscous and inviscid flow problems with non-uniform mesh and curved boundary.

关键词： chapman-Enskog analysis flux solver incompressible flow Navier-Stokes equation lattice Boltzmann equation

Quadrilateral cell-Based Anisotropic Adaptive Solution for the Euler Equations

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communications in computational Physics 2011年第1期9卷 68-88页

作者： H.W.Zheng N.Qin F.c.G.A.Nicolleau c.shu Department of Mechanical Engineering University of SheffieldMappin StreetSheffield S13JDUK Department of Mechanical Engineering National University of Singapore10 Kent Ridge CrescentSingapore 119260.

An anisotropic solution adaptive method based on unstructured quadrilateral meshes for inviscid compressible flows is proposed.The data structure,the directional refinement and coarsening,including the method for initializing the refined new cells,for the anisotropic adaptive method are described.It provides efficient high resolution of flow features,which are aligned with the original quadrilateral mesh structures.Five different cases are provided to show that it could be used to resolve the anisotropic flow features and be applied to model the complex geometry as well as to keep a relative high order of accuracy on an efficient anisotropic mesh.

关键词： Anisotropic adaptive mesh refinement quadrilateral mesh finite volume face-based algorithm HLLc Euler equation

A Boundary condition-Implemented Immersed Boundary-Lattice Boltzmann Method and Its Application for Simulation of Flows Around a circular cylinder

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Advances in Applied Mathematics and Mechanics 2014年第6期6卷 811-829页

作者： X.Wang c.shu J.Wu L.M.Yang Department of Aerodynamics College of Aerospace EngineeringNanjing University of Aeronautics and AstronauticsYudao StreetNanjing 210016China Department of Mechanical Engineering National University of Singapore10 Kent Ridge CrescentSingapore 119260Singapore

A boundary condition-implemented immersed boundary-lattice Boltzmann method(IB-LBM)is presented in this work.The present approach is an improvement to the conventional IB-LBM.In the conventional IB-LBM,the no-slip boundary condition is only approximately satisfied.As a result,there is flow penetration to the solid boundary.Another drawback of conventional IB-LBM is the use of Dirac delta function interpolation,which only has the first order of accuracy.In this work,the no-slip boundary condition is directly implemented,and used to correct the velocity at two adjacent mesh points from both sides of the boundary point.The velocity correction is made through the second-order polynomial interpolation rather than the first-order delta function interpolation.Obviously,the two drawbacks of conventional IB-LBM are removed in the present study.Another important contribution of this paper is to present a simple way to compute the hydrodynamic forces on the boundary from Newton’s second law.To validate the proposed method,the two-dimensional vortex decaying problem and incompressible flow over a circular cylinder are simulated.As shown in the present results,the flow penetration problem is eliminated,and the obtained results compare very well with available data in the literature.

关键词： Immersed boundary method lattice Boltzmann method velocity correction Lagrange interpolation no-slip boundary condition

A three-dimensional gas-kinetic flux solver for simulation of viscous flows with explicit formulations of conservative variables and numerical flux

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Advances in Aerodynamics 2020年第1期2卷 250-277页

作者： Y.Sun L.M.Yang c.shu c.J.Teo Huawei Technologies co. LtdBantianLonggang DistrictShenzhen 518129China Department of Mechanical Engineering National University of Singapore10 Kent Ridge CrescentSingapore 119260Singapore

A truly three-dimensional(3D)gas-kinetic flux solver for simulation of incompressible and compressible viscous flows is presented in this work.By local reconstruction of continuous Boltzmann equation,the inviscid and viscous fluxes across the cell interface are evaluated simultaneously in the solver.Different from conventional gaskinetic scheme,in the present work,the distribution function at cell interface is computed in a straightforward way.As an extension of our previous work(Sun et al.,Journal of computational Physics,300(2015)492–519),the non-equilibrium distribution function is calculated by the difference of equilibrium distribution functions between the cell interface and its surrounding points.As a result,the distribution function at cell interface can be simply calculated and the formulations for computing the conservative flow variables and fluxes can be given explicitly.To validate the proposed flux solver,several incompressible and compressible viscous flows are simulated.Numerical results show that the current scheme can provide accurate numerical results for three-dimensional incompressible and compressible viscous flows.

关键词： 3D flux solver Gas-kinetic scheme Viscous flow Navier-Stokes equations 1 Introduction