Biomedical subjects

Li-Shi Luo

Publications and source records attributed to Li-Shi Luo.

5 recordsLinked to original sources

PubMed2003

Nonexistence of H theorems for the athermal lattice Boltzmann models with polynomial equilibria.

We prove that no H theorem exists for the athermal lattice Boltzmann equation with polynomial equilibria satisfying the conservation laws exactly and explicitly. The proof is demonstrated by using the seven-velocity model in a triangular lattice in two dimensions, and can be readily extended to other lattice Boltzmann models in two and three dimensions. Some issues pertinent to the numerical instabilities of the lattice Boltzmann method are discussed.

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PubMed2003

Theory of the lattice Boltzmann method: two-fluid model for binary mixtures.

A two-fluid lattice Boltzmann model for binary mixtures is developed. The model is derived formally from kinetic theory by discretizing two-fluid Boltzmann equations in which mutual collisions and self-collisions are treated independently. In the resulting lattice Boltzmann model, viscosity and diffusion coefficients can be varied independently by a suitable choice of mutual- and self-collision relaxation-time scales. Further, the proposed model can simulate miscible and immiscible fluids by changing the sign of the mutual-collision term. This is in contrast to most existing single-fluid lattice Boltzmann models that employ a single-relaxation-time scale and hence are restricted to unity Prandtl and Schmidt numbers. The extension of binary mixing model to multiscalar mixing is quite straightforward.

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PubMed2003

Theory of the lattice Boltzmann method: three-dimensional model for linear viscoelastic fluids.

A three-dimensional lattice Boltzmann model with thirty two discrete velocity distribution functions for viscoelastic fluid is presented in this work. The model is based upon the generalized lattice Boltzmann equation constructed in moment space. The nonlinear equilibria of the model have a number of coupling constants that are free parameters. The dispersion equation of the model is analyzed under various conditions to obtain the constraints on the free parameters such that the model satisfies isotropy and Galilean invariance. The macroscopic equations are also derived from the lattice Boltzmann model through the dispersion equation analysis and the Chapman-Enskog analysis. We demonstrate that the dispersion equation analysis can be used as a general and effective means to derive hydrodynamic equations, excluding some nonlinear source terms, from the lattice Boltzmann model, to obtain conditions for its isotropy and Galilean invariance, and to optimize its stability. We show that the hydrodynamic behavior of the lattice Boltzmann model has memory effects, and that in the linear regime, it behaves as a viscoelastic fluid described by the Jeffreys model. Some numerical results to verify the theoretical analysis of the model are also presented.

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PubMed2002

Lattice Boltzmann model for binary mixtures.

An a priori derivation of the lattice Boltzmann equations for binary mixtures is provided by discretizing the Boltzmann equations that govern the evolution of binary mixtures. The present model leads to a set of two-fluid hydrodynamic equations for the mixture. In existing models, employing the single-relaxation-time approximation, the viscosity and diffusion coefficients are coupled through the relaxation parameter tau, thus limited to unity Prandtl number and Schmidt number. In the present model the viscosity and diffusion coefficient are independently controlled by two relaxation parameters, thus enabling the modeling of mixtures with an arbitrary Schmidt number. The theoretical framework developed here can be readily applied to multiple-species mixing.

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PubMed2002

Force evaluation in the lattice Boltzmann method involving curved geometry.

The present work investigates two approaches for force evaluation in the lattice Boltzmann equation: the momentum-exchange method and the stress-integration method on the surface of a body. The boundary condition for the particle distribution functions on curved geometries is handled with second-order accuracy based on our recent works [Mei et al., J. Comput. Phys. 155, 307 (1999); ibid. 161, 680 (2000)]. The stress-integration method is computationally laborious for two-dimensional flows and in general difficult to implement for three-dimensional flows, while the momentum-exchange method is reliable, accurate, and easy to implement for both two-dimensional and three-dimensional flows. Several test cases are selected to evaluate the present methods, including: (i) two-dimensional pressure-driven channel flow; (ii) two-dimensional uniform flow past a column of cylinders; (iii) two-dimensional flow past a cylinder asymmetrically placed in a channel (with vortex shedding); (iv) three-dimensional pressure-driven flow in a circular pipe; and (v) three-dimensional flow past a sphere. The drag evaluated by using the momentum-exchange method agrees well with the exact or other published results.

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