Hudong Chen

Kinetic theory representation of hydrodynamics: a way beyond the Navier-Stokes equation

We present in detail a theoretical framework for representing hydrodynamic systems through a systematic discretization of the Boltzmann kinetic equation. The work is an extension of a previously proposed formulation. Conventional lattice Boltzmann models can be shown to be directly derivable from this systematic approach. Furthermore, we provide here a clear and rigorous procedure for obtaining higher-order approximations to the continuum Boltzmann equation. The resulting macroscopic moment equations at each level of the systematic discretization give rise to the Navier-Stokes hydrodynamics and those beyond. In addition, theoretical indications to the order of accuracy requirements are given for each discrete approximation, for thermohydrodynamic systems, and for fluid systems involving long-range interactions. All these are important for complex and micro-scale flows and are missing in the conventional Navier-Stokes order descriptions. The resulting discrete Boltzmann models are based on a kinetic representation of the fluid dynamics, hence the drawbacks in conventional higher-order hydrodynamic formulations can be avoided.

Realization of Fluid Boundary Conditions via Discrete Boltzmann Dynamics

We describe a novel way based on lattice-Boltzmann representation for realizing hydrodynamic boundary conditions at a solid surface. It is shown that using this approach the resulting physics properties are independent of the position and the orientation of the surface with respect to the lattice mesh. The fluxes of mass, energy as well as both normal and tangential momenta can be accurately controlled to correspond to various fluid dynamics situations.

Numerical study of flow past an impulsively started cylinder by the lattice-Boltzmann method

In this paper a systematic numerical study of flow past an impulsively started circular cylinder at low and moderate Reynolds numbers using a lattice-Boltzmann algorithmic approach is presented together with an extended volumetric boundary scheme. Results agree well with some well-known previous works. It is demonstrated that in the nearly incompressible limit, this approach is able to provide accurate direct numerical simulations of unsteady flows with curved geometry.

Digital Physics Approach to Computational Fluid Dynamics: Some Basic Theoretical Features

We present an outline description of some fundamental theoretical properties in the Digital Physics lattice-gas algorithm.

Colloquium: Role of the H theorem in lattice Boltzmann hydrodynamic simulations

In the last decade, minimal kinetic models, and primarily the lattice Boltzmann equation, have met with significant success in the simulation of complex hydrodynamic phenomena, ranging from slow flows in grossly irregular geometries to fully developed turbulence, to flows with dynamic phase transitions. Besides their practical value as efficient computational tools for the dynamics of complex systems, these minimal models may also represent a new conceptual paradigm in modern computational statistical mechanics: instead of proceeding bottom-up from the underlying microdynamic systems, these minimal kinetic models are built top-down starting from the macroscopic target equations. This procedure can provide dramatic advantages, provided the essential physics is not lost along the way. For dissipative systems, one essential requirement is compliance with the second law of thermodynamics. In this Colloquium, the authors present a chronological survey of the main ideas behind the lattice Boltzmann method, with special focus on the role played by the H theorem in enforcing compliance of the method with macroscopic evolutionary constraints (the second law) as well as in serving as a numerically stable computational tool for fluid flows and other dissipative systems out of equilibrium.

Lattice Boltzmann method for simulations of liquid-vapor thermal flows.

We present a lattice Boltzmann method that has the capability of simulating thermodynamic multiphase flows. This approach is fully thermodynamically consistent at the macroscopic level. Using this method, the liquid-vapor boiling process, including liquid-vapor formation and coalescence together with a full coupling of temperature, is simulated.

Efficient kinetic method for fluid simulation beyond the Navier-Stokes equation

We present a further theoretical extension to the kinetic-theory-based formulation of the lattice Boltzmann method of Shan [J. Fluid Mech. 550, 413 (2006)]. In addition to the higher-order projection of the equilibrium distribution function and a sufficiently accurate Gauss-Hermite quadrature in the original formulation, a regularization procedure is introduced in this paper. This procedure ensures a consistent order of accuracy control over the nonequilibrium contributions in the Galerkin sense. Using this formulation, we construct a specific lattice Boltzmann model that accurately incorporates up to third-order hydrodynamic moments. Numerical evidence demonstrates that the extended model overcomes some major defects existing in conventionally known lattice Boltzmann models, so that fluid flows at finite Knudsen number Kn can be more quantitatively simulated. Results from force-driven Poiseuille flow simulations predict the Knudsens minimum and the asymptotic behavior of flow flux at large Kn.

Lattice Boltzmann method with self-consistent thermo-hydrodynamic equilibria

Lattice kinetic equations incorporating the effects of external/internal force fields via a shift of the local fields in the local equilibria are placed within the framework of continuum kinetic theory. The mathematical treatment reveals that in order to be consistent with the correct thermo-hydrodynamical description, temperature must also be shifted, besides momentum. New perspectives for the formulation of thermo-hydrodynamic lattice kinetic models of non-ideal fluids are then envisaged. It is also shown that on the lattice, the definition of the macroscopic temperature requires the inclusion of new terms directly related to discrete effects. The theoretical treatment is tested against a controlled case with a non-ideal equation of state.

Lattice-Boltzmann model for interacting amphiphilic fluids

We develop our recently proposed lattice-Boltzmann method for the nonequilibrium dynamics of amphiphilic fluids [H. Chen, B. M. Boghosian, P. V. Coveney, and M. Nekovee, Proc. R. Soc. London, Ser. A 456, 2043 (2000)]. Our method maintains an orientational degree of freedom for the amphiphilic species and models fluid interactions at a microscopic level by introducing self-consistent mean-field forces between the particles into the lattice-Boltzmann dynamics, in a way that is consistent with kinetic theory. We present the results of extensive simulations in two dimensions which demonstrate the ability of our model to capture the correct phenomenology of binary and ternary amphiphilic fluids.

H-theorem and origins of instability in thermal lattice Boltzmann models

In this paper, we present an H-theorem for lattice Boltzmann systems. This is a straightforward extension from that for lattice gas systems obeying generalized semi-detailed balance. We point out that the origin of reduced stabilities seen in thermal lattice Boltzmann models is related to the lack of a global H-theorem.