This paper opens a series of papers aimed at finalizing the development of the lattice Boltzmann method for complex hydrodynamic systems.The lattice Boltzmann method is introduced at the elementary level of the linear...This paper opens a series of papers aimed at finalizing the development of the lattice Boltzmann method for complex hydrodynamic systems.The lattice Boltzmann method is introduced at the elementary level of the linear advection equation.Details are provided on lifting the target macroscopic equations to a kinetic equation,and,after that,to the fully discrete lattice Boltzmann scheme.The over-relaxation method is put forward as a cornerstone of the second-order temporal discretization,and its enhancement with the use of the entropy estimate is explained in detail.A new asymptotic expansion of the entropy estimate is derived,and implemented in the sample code.It is shown that the lattice Boltzmann method provides a computationally efficient way of numerically solving the advection equation with a controlled amount of numerical dissipation,while retaining positivity.展开更多
Concepts of the lattice Boltzmann method are discussed in detail for the one-dimensional kinetic model.Various techniques of constructing lattice Boltzmann models are discussed,and novel collision integrals are derive...Concepts of the lattice Boltzmann method are discussed in detail for the one-dimensional kinetic model.Various techniques of constructing lattice Boltzmann models are discussed,and novel collision integrals are derived.Geometry of the ki-netic space and the role of the thermodynamic projector is elucidated.展开更多
An alternate BGK type formulation of the Enskog equation has been recently proposed[1].It was shown that the new model has a valid H-theorem and correct thermal conductivity.We propose Lattice Boltzmann(LB)formulation...An alternate BGK type formulation of the Enskog equation has been recently proposed[1].It was shown that the new model has a valid H-theorem and correct thermal conductivity.We propose Lattice Boltzmann(LB)formulation of this new EnskogBGK model.The molecular nature of the model is verified in case of shear flow by comparing the predicted normal stress behavior by the current model with the prediction of molecular dynamics simulations.We extend the model for multiphase flow by incorporating attractive part as Vlasov type force.To validate multiphase formulation,the results of 3D simulations of a condensing bubble in a periodic box are presented.展开更多
The exact solution to the hierarchy of nonlinear lattice Boltzmann kinetic equations,for the stationary planar Couette flow for any Knudsen number was presented by S.Ansumali et al.[Phys.Rev.Lett.,98(2007),124502].In ...The exact solution to the hierarchy of nonlinear lattice Boltzmann kinetic equations,for the stationary planar Couette flow for any Knudsen number was presented by S.Ansumali et al.[Phys.Rev.Lett.,98(2007),124502].In this paper,simulation results at a non-vanishing value of the Knudsen number are compared with the closed-form solutions for the higher-order moments.The order of convergence to the exact solution is also studied.The lattice Boltzmann simulations are in excellent agreement with the exact solution.展开更多
In this paper,we highlight the benefits resulting from imposing energyconserving equilibria in entropic lattice Boltzmann models for isothermal flows.The advantages are documented through a series of numerical simulat...In this paper,we highlight the benefits resulting from imposing energyconserving equilibria in entropic lattice Boltzmann models for isothermal flows.The advantages are documented through a series of numerical simulations,such as TaylorGreen vortices,cavity flow and flow past a sphere.展开更多
文摘This paper opens a series of papers aimed at finalizing the development of the lattice Boltzmann method for complex hydrodynamic systems.The lattice Boltzmann method is introduced at the elementary level of the linear advection equation.Details are provided on lifting the target macroscopic equations to a kinetic equation,and,after that,to the fully discrete lattice Boltzmann scheme.The over-relaxation method is put forward as a cornerstone of the second-order temporal discretization,and its enhancement with the use of the entropy estimate is explained in detail.A new asymptotic expansion of the entropy estimate is derived,and implemented in the sample code.It is shown that the lattice Boltzmann method provides a computationally efficient way of numerically solving the advection equation with a controlled amount of numerical dissipation,while retaining positivity.
基金support by the BFE Project 100862.S.S.C.was supported by the ETH Project 0-20280-05.
文摘Concepts of the lattice Boltzmann method are discussed in detail for the one-dimensional kinetic model.Various techniques of constructing lattice Boltzmann models are discussed,and novel collision integrals are derived.Geometry of the ki-netic space and the role of the thermodynamic projector is elucidated.
基金ICAM-I2CAM,1 Shields Avenue,Davis,CA 95616 for travel support through NSF grant number DMR-0844115 for attending DSFD2012 where this work was presentedDepartment of Science and Technology(DST),India for providing computational resources via Ramanujan Fellowship grant.
文摘An alternate BGK type formulation of the Enskog equation has been recently proposed[1].It was shown that the new model has a valid H-theorem and correct thermal conductivity.We propose Lattice Boltzmann(LB)formulation of this new EnskogBGK model.The molecular nature of the model is verified in case of shear flow by comparing the predicted normal stress behavior by the current model with the prediction of molecular dynamics simulations.We extend the model for multiphase flow by incorporating attractive part as Vlasov type force.To validate multiphase formulation,the results of 3D simulations of a condensing bubble in a periodic box are presented.
基金The authors acknowledge useful discussions with Dr.I.V.Karlin.N.I.Prasianakis was supported by the BFE project 103078.S.
文摘The exact solution to the hierarchy of nonlinear lattice Boltzmann kinetic equations,for the stationary planar Couette flow for any Knudsen number was presented by S.Ansumali et al.[Phys.Rev.Lett.,98(2007),124502].In this paper,simulation results at a non-vanishing value of the Knudsen number are compared with the closed-form solutions for the higher-order moments.The order of convergence to the exact solution is also studied.The lattice Boltzmann simulations are in excellent agreement with the exact solution.
基金Department of Science and Technology(DST),India for providing computational resources via Ramanujan Fellowship grantproviding financial support and kind hospitality through the Raman Chair of the Indian Academy of Sciences.
文摘In this paper,we highlight the benefits resulting from imposing energyconserving equilibria in entropic lattice Boltzmann models for isothermal flows.The advantages are documented through a series of numerical simulations,such as TaylorGreen vortices,cavity flow and flow past a sphere.
