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Diffusivity Of Two-Component Isothermal Finite Difference Lattice Boltzmann Models

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  • VICTOR SOFONEA

    (Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA;
    Laboratory for Numerical Simulation and Parallel Computing in Fluid Mechanics, Center for Fundamental and Advanced Technical Research, Romanian Academy, Bd. Mihai Viteazul 24, RO — 300223 Timişoara, Romania)

  • ROBERT F. SEKERKA

    (Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA)

Abstract

Diffusion equations are derived for an isothermal lattice Boltzmann model with two components. The first-order upwind finite difference scheme is used to solve the evolution equations for the distribution functions. When using this scheme, the numerical diffusivity, which is a spurious diffusivity in addition to the physical diffusivity, is proportional to the lattice spacing and significantly exceeds the physical value of the diffusivity if the number of lattice nodes per unit length is too small. Flux limiter schemes are introduced to overcome this problem. Empirical analysis of the results of flux limiter schemes shows that the numerical diffusivity is very small and depends quadratically on the lattice spacing.

Suggested Citation

  • Victor Sofonea & Robert F. Sekerka, 2005. "Diffusivity Of Two-Component Isothermal Finite Difference Lattice Boltzmann Models," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 16(07), pages 1075-1090.
    • Handle: RePEc:wsi:ijmpcx:v:16:y:2005:i:07:n:s0129183105007741
    DOI: 10.1142/S0129183105007741
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