The Experts below are selected from a list of 249 Experts worldwide ranked by ideXlab platform

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

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

  • discretization of the velocity space in the solution of the Boltzmann Equation
    Physical Review Letters, 1998
    Co-Authors: Xiaowen Shan
    Abstract:

    We point out an equivalence between the discrete velocity method of solving the Boltzmann Equation, of which the lattice Boltzmann Equation method is a special example, and the approximations to the Boltzmann Equation by a Hermite polynomial expansion. Discretizing the Boltzmann Equation with a Bhatnagar-Gross-Krook collision term at the velocities that correspond to the nodes of a Hermite quadrature is shown to be equivalent to truncating the Hermite expansion of the distribution function to the corresponding order. The truncated part of the distribution has no contribution to the moments of low orders and is negligible at small Mach numbers.

  • 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,

Klaus Hornberger - One of the best experts on this subject based on the ideXlab platform.

  • Quantum linear Boltzmann Equation
    Physics Reports, 2009
    Co-Authors: Bassano Vacchini, Klaus Hornberger
    Abstract:

    We review the quantum version of the linear Boltzmann Equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic derivation of this Lindblad master Equation is presented, based on the requirement of translation-covariance and on the relation to the classical linear Boltzmann Equation. After analyzing its general symmetry properties and the associated relaxation dynamics, we discuss a quantum Monte Carlo method for its numerical solution. We then review important limiting forms of the quantum linear Boltzmann Equation, such as the case of quantum Brownian motion and pure collisional decoherence, as well as the application to matter wave optics. Finally, we point to the incorporation of quantum degeneracies and self-interactions in the gas by relating the Equation to the dynamic structure factor of the ambient medium, and we provide an extension of the Equation to include internal degrees of freedom.

Seok-bae Yun - One of the best experts on this subject based on the ideXlab platform.

  • The Relativistic Quantum Boltzmann Equation Near Equilibrium
    Archive for Rational Mechanics and Analysis, 2021
    Co-Authors: Gi-chan Bae, Jin Woo Jang, Seok-bae Yun
    Abstract:

    The relativistic quantum Boltzmann Equation (or the relativistic Uehling–Uhlenbeck Equation) describes the dynamics of single-species fast-moving quantum particles. With the recent development of relativistic quantum mechanics, the relativistic quantum Boltzmann Equation has been widely used in physics and engineering, for example in the quantum collision experiments and the simulations of electrons in graphene. In spite of such importance, there has, to the best of our knowledge, been no mathematical theory on the existence of solutions to the relativistic quantum Boltzmann Equation. In this paper, we prove the global existence of a unique classical solution to the relativistic Boltzmann Equation for both bosons and fermions, when the initial distribution is nearby a global equilibrium.

Bernt Wennberg - One of the best experts on this subject based on the ideXlab platform.

  • Stability and exponential convergence for the Boltzmann Equation
    Archive for Rational Mechanics and Analysis, 1995
    Co-Authors: Bernt Wennberg
    Abstract:

    We prove existence, uniqueness and stability for solutions of the nonlinear Boltzmann Equation in a periodic box in the case when the initial data are sufficiently close to a spatially homogeneous function. The results are given for a range of spaces, including L ^1, and extend previous results in L ^∞ for the non-homogeneous Equation, as well as the more developed L ^ p -theory for the spatially homogeneous Boltzmann Equation. We also give new L ^∞-estimates for the spatially homogeneous Equation in the case of Maxwellian interactions.

  • Stability and exponential convergence for the Boltzmann Equation
    Archive for Rational Mechanics and Analysis, 1995
    Co-Authors: Bernt Wennberg
    Abstract:

    We prove existence, uniqueness and stability for solutions of the nonlinear Boltzmann Equation in a periodic box in the case when the initial data are sufficiently close to a spatially homogeneous function. The results are given for a range of spaces, including L1, and extend previous results in L∞ for the non-homogeneous Equation, as well as the more developed Lp-theory for the spatially homogeneous Boltzmann Equation.