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Xiaowen Shan - One of the best experts on this subject based on the ideXlab platform.

  • pressure tensor calculation in a class of Nonideal Gas lattice boltzmann models
    Physical Review E, 2008
    Co-Authors: Xiaowen Shan
    Abstract:

    In Nonideal Gas lattice Boltzmann (LB) models, obtaining the correct form of the pressure tensor is essential in determining many of the statistical mechanical properties such as the surface tension and the density profile. Here we outline a general approach for calculating the pressure tensor in LB models with interactions beyond nearest neighbors. The statistical mechanical properties calculated from such a pressure tensor are shown to agree very well with those measured from numerical experiments. Comparisons with alternative theories are also made.

  • discrete boltzmann equation model for Nonideal Gases
    Physical Review E, 1998
    Co-Authors: Xiaowen Shan, Gary D Doolen
    Abstract:

    Computer simulations of fluid dynamical problems involving fluid interfaces and phase transitions are of both fundamental and practical importance. Traditional computational fluid dynamics ~CFD! methods for solving macroscopic hydrodynamic equations have many difficulties in this area. For instance, fluid interfaces often undergo topological change due to both coalescence and phase transitions. In problems where the capillary effect is important, high resolution is required for accurate computation of interface curvature. The treatment of these problems using a Navier-Stokes solver is cumbersome, if not impossible, in many situations. The macroscopic motion of a fluid can also be solved by computing motions of its constituent particles. Since the complexity of the Nonideal-Gas fluid systems is essentially due to the microscopic interparticle interaction, particle methods such as molecular dynamics can simulate complex fluid phenomena naturally by implementing the correct interparticle potential. However, these methods are very inefficient for fluid simulations. At the mesoscopic level, the lattice-Boltzmann-equation ~LBE! method simulates the motion of fluids by following the evolution of a lattice Boltzmann equation that governs the behavior of the single-particle distribution function. It was found that solving the LBE directly is an efficient and accurate method for simulating fluid motion @1#. More importantly, the interparticle interaction can be easily incorporated into the LBE method to form a model that can simulate macroscopic complex fluid phenomena at least as efficiently as the conventional CFD methods solve the hydrodynamic equations for simple fluids @2#. Although the LBE method has shown its ability to simulate complex fluids, a recent study @3# shows that this method can be greatly improved if one can establish the relationship between the LBE and the continuous Boltzmann equation @3#. Historically, the continuous Boltzmann equation has mainly been used to solve supersonic flows @4#. This is partially due to both the extreme complexity of the collision kernel when dealing with dense, interacting particles and the tremendous computer resources required to resolve the sixdimensional distribution function. In this paper, we propose a computational scheme for the simulation of Nonideal Gases based on the continuous Boltzmann equation using a singlerelaxation-time approximation, also known as the BhatnagarGross-Krook ~BGK! collision model @5#. The interparticle attraction is treated using a mean-field approximation in the same way that the Coulomb interaction among the charged particles of a plasma is treated in the Vlasov equation @5#. Following the work of Enskog, the effect of the exclusion volume is taken into account by an additional term in the collision operator. The final Boltzmann equation is then discretized in the velocity space in a way that guarantees that the Navier-Stokes equation is obtained at the macroscopic level. This discretization is similar to the truncation made in the well-known 13-moment method of Grad @6#. The previously proposed Nonideal LBE model @2# can be obtained with only minor differences. The present derivation allows the LBE model to be implemented on nonuniform grids. The ‘‘interaction potential’’ introduced previously now has a clear connection with the interparticle pairwise potential in real fluids. Analysis of some other schemes @7,8# for incorporating interparticle forces into LBE models in the framework of the present derivation shows that anisotropy is a consequence of an inappropriate intermolecular interaction. We start from the following Boltzmann equation in which the collision term is replaced by the BGK collision model,

  • evaluation of two lattice boltzmann models for multiphase flows
    Journal of Computational Physics, 1997
    Co-Authors: Shuling Hou, Gary D Doolen, Xiaowen Shan, Qisu Zou, Wendy E Soll
    Abstract:

    Two lattice Boltzmann models for multiphase flows, the immiscible fluid model proposed by Rothman and Keller (RÂ?K) and the multicomponent Nonideal Gas lattice Boltzmann model by Shan and Chen (SÂ?C), are studied numerically to compare their abilities to simulate the physics of multiphase flows. The test problem is the simulation of a static bubble. Isotropy, strength of surface tension, thickness of the interface, spurious currents, Laplace's law, and steadiness of the bubble are examined. The results show that the SÂ?C model is a major improvement over the RÂ?K model.

  • simulation of Nonideal Gases and liquid Gas phase transitions by the lattice boltzmann equation
    Physical Review E, 1994
    Co-Authors: Xiaowen Shan, Hudong Chen
    Abstract:

    We describe in detail a recently proposed lattice-Boltzmann model [X. Shan and H. Chen, Phys. Rev. E 47, 1815 (1993)] for simulating flows with multiple phases and components. In particular, the focus is on the modeling of one-component fluid systems which obey Nonideal Gas equations of state and can undergo a liquid-Gas-type phase transition. The model is shown to be momentum conserving. From the microscopic mechanical stability condition, the densities in bulk liquid and Gas phases are obtained as functions of a temperaturelike parameter. Comparisons with the thermodynamic theory of phase transitions show that the lattice-Boltzmann-equation model can be made to correspond exactly to an isothermal process. The density profile in the liquid-Gas interface is also obtained as a function of the temperaturelike parameter and is shown to be isotropic. The surface tension, which can be changed independently, is calculated. The analytical conclusions are verified by numerical simulations.

  • lattice boltzmann model for simulating flows with multiple phases and components
    Physical Review A, 1993
    Co-Authors: Xiaowen Shan, Hudong Chen
    Abstract:

    A lattice Boltzmann model is developed which has the ability to simulate flows containing multiple phases and components. Each of the components can be immiscible with the others and can have different mass values. The equilibrium state of each component can have a Nonideal Gas equation of state at a prescribed temperature exhibiting thermodynamic phase transitions. The scheme incorporated in this model is the introduction of an interparticle potential. The dynamical rules in this model are local so it is highly efficient to compute on massively parallel computers. This model has many application in large-scale numerical simulations of various types of fluid flows

Hudong Chen - One of the best experts on this subject based on the ideXlab platform.

  • simulation of Nonideal Gases and liquid Gas phase transitions by the lattice boltzmann equation
    Physical Review E, 1994
    Co-Authors: Xiaowen Shan, Hudong Chen
    Abstract:

    We describe in detail a recently proposed lattice-Boltzmann model [X. Shan and H. Chen, Phys. Rev. E 47, 1815 (1993)] for simulating flows with multiple phases and components. In particular, the focus is on the modeling of one-component fluid systems which obey Nonideal Gas equations of state and can undergo a liquid-Gas-type phase transition. The model is shown to be momentum conserving. From the microscopic mechanical stability condition, the densities in bulk liquid and Gas phases are obtained as functions of a temperaturelike parameter. Comparisons with the thermodynamic theory of phase transitions show that the lattice-Boltzmann-equation model can be made to correspond exactly to an isothermal process. The density profile in the liquid-Gas interface is also obtained as a function of the temperaturelike parameter and is shown to be isotropic. The surface tension, which can be changed independently, is calculated. The analytical conclusions are verified by numerical simulations.

  • lattice boltzmann model for simulating flows with multiple phases and components
    Physical Review A, 1993
    Co-Authors: Xiaowen Shan, Hudong Chen
    Abstract:

    A lattice Boltzmann model is developed which has the ability to simulate flows containing multiple phases and components. Each of the components can be immiscible with the others and can have different mass values. The equilibrium state of each component can have a Nonideal Gas equation of state at a prescribed temperature exhibiting thermodynamic phase transitions. The scheme incorporated in this model is the introduction of an interparticle potential. The dynamical rules in this model are local so it is highly efficient to compute on massively parallel computers. This model has many application in large-scale numerical simulations of various types of fluid flows

  • Lattice Gas models for Nonideal Gas fluids
    Physica D: Nonlinear Phenomena, 1991
    Co-Authors: Shiyi Chen, Gary D Doolen, Hudong Chen, Harvey A. Rose, Helmut R. Brand
    Abstract:

    Abstract A lattice Gas model with a Nonideal Gas equation of state is presented. Transitions between the solid and Gas phase are described. Computer simulations of applications of this model to shock waves are discussed. Generalization of this model to liquid crystal flow is also outlined.

Gary D Doolen - One of the best experts on this subject based on the ideXlab platform.

  • discrete boltzmann equation model for Nonideal Gases
    Physical Review E, 1998
    Co-Authors: Xiaowen Shan, Gary D Doolen
    Abstract:

    Computer simulations of fluid dynamical problems involving fluid interfaces and phase transitions are of both fundamental and practical importance. Traditional computational fluid dynamics ~CFD! methods for solving macroscopic hydrodynamic equations have many difficulties in this area. For instance, fluid interfaces often undergo topological change due to both coalescence and phase transitions. In problems where the capillary effect is important, high resolution is required for accurate computation of interface curvature. The treatment of these problems using a Navier-Stokes solver is cumbersome, if not impossible, in many situations. The macroscopic motion of a fluid can also be solved by computing motions of its constituent particles. Since the complexity of the Nonideal-Gas fluid systems is essentially due to the microscopic interparticle interaction, particle methods such as molecular dynamics can simulate complex fluid phenomena naturally by implementing the correct interparticle potential. However, these methods are very inefficient for fluid simulations. At the mesoscopic level, the lattice-Boltzmann-equation ~LBE! method simulates the motion of fluids by following the evolution of a lattice Boltzmann equation that governs the behavior of the single-particle distribution function. It was found that solving the LBE directly is an efficient and accurate method for simulating fluid motion @1#. More importantly, the interparticle interaction can be easily incorporated into the LBE method to form a model that can simulate macroscopic complex fluid phenomena at least as efficiently as the conventional CFD methods solve the hydrodynamic equations for simple fluids @2#. Although the LBE method has shown its ability to simulate complex fluids, a recent study @3# shows that this method can be greatly improved if one can establish the relationship between the LBE and the continuous Boltzmann equation @3#. Historically, the continuous Boltzmann equation has mainly been used to solve supersonic flows @4#. This is partially due to both the extreme complexity of the collision kernel when dealing with dense, interacting particles and the tremendous computer resources required to resolve the sixdimensional distribution function. In this paper, we propose a computational scheme for the simulation of Nonideal Gases based on the continuous Boltzmann equation using a singlerelaxation-time approximation, also known as the BhatnagarGross-Krook ~BGK! collision model @5#. The interparticle attraction is treated using a mean-field approximation in the same way that the Coulomb interaction among the charged particles of a plasma is treated in the Vlasov equation @5#. Following the work of Enskog, the effect of the exclusion volume is taken into account by an additional term in the collision operator. The final Boltzmann equation is then discretized in the velocity space in a way that guarantees that the Navier-Stokes equation is obtained at the macroscopic level. This discretization is similar to the truncation made in the well-known 13-moment method of Grad @6#. The previously proposed Nonideal LBE model @2# can be obtained with only minor differences. The present derivation allows the LBE model to be implemented on nonuniform grids. The ‘‘interaction potential’’ introduced previously now has a clear connection with the interparticle pairwise potential in real fluids. Analysis of some other schemes @7,8# for incorporating interparticle forces into LBE models in the framework of the present derivation shows that anisotropy is a consequence of an inappropriate intermolecular interaction. We start from the following Boltzmann equation in which the collision term is replaced by the BGK collision model,

  • evaluation of two lattice boltzmann models for multiphase flows
    Journal of Computational Physics, 1997
    Co-Authors: Shuling Hou, Gary D Doolen, Xiaowen Shan, Qisu Zou, Wendy E Soll
    Abstract:

    Two lattice Boltzmann models for multiphase flows, the immiscible fluid model proposed by Rothman and Keller (RÂ?K) and the multicomponent Nonideal Gas lattice Boltzmann model by Shan and Chen (SÂ?C), are studied numerically to compare their abilities to simulate the physics of multiphase flows. The test problem is the simulation of a static bubble. Isotropy, strength of surface tension, thickness of the interface, spurious currents, Laplace's law, and steadiness of the bubble are examined. The results show that the SÂ?C model is a major improvement over the RÂ?K model.

  • Lattice Gas models for Nonideal Gas fluids
    Physica D: Nonlinear Phenomena, 1991
    Co-Authors: Shiyi Chen, Gary D Doolen, Hudong Chen, Harvey A. Rose, Helmut R. Brand
    Abstract:

    Abstract A lattice Gas model with a Nonideal Gas equation of state is presented. Transitions between the solid and Gas phase are described. Computer simulations of applications of this model to shock waves are discussed. Generalization of this model to liquid crystal flow is also outlined.

Lishi Luo - One of the best experts on this subject based on the ideXlab platform.

Wendy E Soll - One of the best experts on this subject based on the ideXlab platform.

  • evaluation of two lattice boltzmann models for multiphase flows
    Journal of Computational Physics, 1997
    Co-Authors: Shuling Hou, Gary D Doolen, Xiaowen Shan, Qisu Zou, Wendy E Soll
    Abstract:

    Two lattice Boltzmann models for multiphase flows, the immiscible fluid model proposed by Rothman and Keller (RÂ?K) and the multicomponent Nonideal Gas lattice Boltzmann model by Shan and Chen (SÂ?C), are studied numerically to compare their abilities to simulate the physics of multiphase flows. The test problem is the simulation of a static bubble. Isotropy, strength of surface tension, thickness of the interface, spurious currents, Laplace's law, and steadiness of the bubble are examined. The results show that the SÂ?C model is a major improvement over the RÂ?K model.