Error Analysis for the Interpolation-Supplemented Lattice-Boltzmann Equation Scheme

The numerical error of the interpolation-supplemented lattice-Boltzmann equation (ISLBE) scheme is theoretically analyzed. The ISLBE is proved to recover the Navier–Stokes equation as long as a second order interpolation scheme is used and the flow domain is appropriately discretized. Using a linear interpolation scheme will inevitably generate the numerical diffusivity and viscosity, making the ISLBE scheme unable to simulate the Navier–Stokes equation correctly. The analysis is consistent with previous numerical experiments.

[1]  S. Succi,et al.  The lattice Boltzmann equation on irregular lattices , 1992 .

[2]  Shiyi Chen,et al.  Stability Analysis of Lattice Boltzmann Methods , 1993, comp-gas/9306001.

[3]  Shiyi Chen,et al.  Lattice Boltzmann computational fluid dynamics in three dimensions , 1992 .

[4]  P. Bhatnagar,et al.  A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems , 1954 .

[5]  J. Jiménez,et al.  Boltzmann Approach to Lattice Gas Simulations , 1989 .

[6]  S. Wolfram.  Cellular automaton fluids 1: Basic theory , 1986 .

[7]  Matthaeus,et al.  Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[8]  Y. Pomeau,et al.  Lattice-gas automata for the Navier-Stokes equation. , 1986, Physical review letters.

[9]  James D. Sterling,et al.  Accuracy of Discrete-Velocity BGK Models for the Simulation of the Incompressible Navier-Stokes Equations , 1993, comp-gas/9307003.

[10]  Kun Xu,et al.  Numerical Navier-Stokes solutions from gas kinetic theory , 1994 .

[11]  Sauro Succi,et al.  Challenges in lattice Boltzmann computing , 1995 .

[12]  Li-Shi Luo,et al.  Some Progress in Lattice Boltzmann Method. Part I. Nonuniform Mesh Grids , 1996 .

[13]  S. Succi,et al.  The finite volume formulation of the Lattice Boltzmann equation , 1994 .

[14]  Xiaoyi He,et al.  Lattice Boltzmann Method on Curvilinear Coordinates System , 1997 .

[15]  Y. Qian,et al.  Lattice BGK Models for Navier-Stokes Equation , 1992 .