Nonlinear Stability of Compressible Thermal Lattice BGK Models

The nonlinear stability of thermal lattice BGK models is examined by means of computer simulation for the case of one- and two- dimensional compressible flows. It is shown that in one dimension (1D) the method is stable on a sizeable range of flow speeds and temperatures. In two dimensions (2D) the method is stable even in the presence of negative distribution functions, but on a smaller stability domain. The computational efficiency of the method compares favorably with classical algorithms for compressible flows, such as the $\lambda$-scheme and the Lax--Wendroff scheme.

[1]  C. Hirsch,et al.  Numerical Computation of Internal and External Flows. By C. HIRSCH. Wiley. Vol. 1, Fundamentals of Numerical Discretization. 1988. 515 pp. £60. Vol. 2, Computational Methods for Inviscid and Viscous Flows. 1990, 691 pp. £65. , 1991, Journal of Fluid Mechanics.

[2]  Li-Shi Luo,et al.  Lattice-gas automata and lattice Boltzmann equations for two-dimensional hydrodynamics , 1993 .

[3]  Sauro Succi,et al.  Recent Advances in Lattice Boltzmann Computing , 1995 .

[4]  Sauro Succi,et al.  THERMOHYDRODYNAMIC LATTICE BGK SCHEMES WITH NON-PERTURBATIVE EQUILIBRIA , 1998 .

[5]  Alejandro L. Garcia,et al.  Stabilization of thermal lattice Boltzmann models , 1995 .

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

[7]  Chen,et al.  Lattice Boltzmann thermohydrodynamics. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  Sauro Succi,et al.  The lattice Boltzmann equation: a new tool for computational fluid-dynamics , 1991 .

[9]  Kalos Mh.  Correlated pairs in model fermion Monte Carlo calculations. , 1996 .

[10]  Pierre Lallemand,et al.  Lattice Gas Hydrodynamics in Two and Three Dimensions , 1987, Complex Syst..

[11]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[12]  Frisch,et al.  Lattice gas automata for the Navier-Stokes equations. a new approach to hydrodynamics and turbulence , 1989 .

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

[14]  Yue-Hong Qian,et al.  Simulating thermohydrodynamics with lattice BGK models , 1993 .

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

[16]  Gino Moretti,et al.  The λ-scheme , 1979 .