Lattice Boltzmann method for one and two-dimensional Burgers equation ☆

[1]  T. G. Cowling,et al.  The mathematical theory of non-uniform gases , 1939 .

[2]  J. Burgers.  A mathematical model illustrating the theory of turbulence , 1948 .

[3]  J. Cole.  On a quasi-linear parabolic equation occurring in aerodynamics , 1951 .

[4]  R. Pletcher,et al.  Computational Fluid Mechanics and Heat Transfer , 1984 .

[5]  A. Westerberg,et al.  An implementation of a moving finite element method , 1986 .

[6]  S. Succi,et al.  Three-Dimensional Flows in Complex Geometries with the Lattice Boltzmann Method , 1989 .

[7]  Chen,et al.  Lattice Boltzmann model for compressible fluids , 1992 .

[8]  Fred Wubs,et al.  An explicit-implicit method for a class of time-dependent partial differential equations , 1992 .

[9]  R. Benzi,et al.  The lattice Boltzmann equation: theory and applications , 1992 .

[10]  Skordos,et al.  Initial and boundary conditions for the lattice Boltzmann method. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  A. Ladd.  Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results , 1993, Journal of Fluid Mechanics.

[12]  A. Ladd.  Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation , 1993, Journal of Fluid Mechanics.

[13]  Shan,et al.  Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  Bracy H. Elton.  Comparisons of Lattice Boltzmann and Finite Difference Methods for a Two-Dimensional Viscous Burgers Equation , 1996, SIAM J. Sci. Comput..

[15]  Robert S. Bernard,et al.  Boundary conditions for the lattice Boltzmann method , 1996 .

[16]  O. Goyon,et al.  Multilevel schemes for solving unsteady equations , 1996 .

[17]  O. Filippova,et al.  Lattice-Boltzmann simulation of gas-particle flow in filters , 1997 .

[18]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[19]  Chen Yaosong,et al.  Simple lattice Boltzmann model for simulating flows with shock wave , 1999 .

[20]  Samir F. Radwan.  On the Fourth-Order Accurate Compact ADI Scheme for Solving the Unsteady Nonlinear Coupled Burgers’ Equations , 1999 .

[21]  Guang-wu Yan,et al.  Recovery of the Solitons Using a Lattice Boltzmann Model , 1999 .

[22]  Yang Guangwu.  A Lattice Boltzmann Equation for Waves , 2000 .

[23]  D. Wolf-Gladrow.  Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An Introduction , 2000 .

[24]  Guangwu Yan,et al.  Lattice Bhatnagar—Gross—Krook model for the Lorenz attractor , 2001 .

[25]  Luo Li-Shi,et al.  Theory of the lattice Boltzmann method: Lattice Boltzmann models for non-ideal gases , 2001 .

[26]  A. Refik Bahadir,et al.  A fully implicit finite-difference scheme for two-dimensional Burgers' equations , 2003, Appl. Math. Comput..

[27]  Jeffrey Yepez,et al.  Entropic lattice Boltzmann model for Burgers's equation , 2004, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[28]  A New Lattice Boltzmann Model for KdV-Burgers Equation , 2005 .

[29]  A. A. Soliman,et al.  Variational iteration method for solving Burger's and coupled Burger's equations , 2005 .

[30]  Z. Horii,et al.  Mass transport theory for the Toda lattices, dispersive and dissipative , 2005 .

[31]  E. N. Aksan,et al.  Quadratic B-spline finite element method for numerical solution of the Burgers' equation , 2006, Appl. Math. Comput..

[32]  K. M. Bryden,et al.  Parallel performance and accuracy of lattice Boltzmann and traditional finite difference methods for solving the unsteady two-dimensional Burger's equation , 2006 .

[33]  John Abraham,et al.  Three-dimensional multi-relaxation time (MRT) lattice-Boltzmann models for multiphase flow , 2007, J. Comput. Phys..

[34]  Guangwu Yan,et al.  A multi-energy-level lattice Boltzmann model for the compressible Navier-Stokes equations , 2007 .

[35]  N. Kudryashov,et al.  Polygons of differential equations for finding exact solutions , 2007 .

[36]  Yali Duan,et al.  Lattice Boltzmann model for two-dimensional unsteady Burgers' equation , 2007 .