Rectangular lattice Boltzmann model for nonlinear convection–diffusion equations

Rectangular lattice Boltzmann model for nonlinear convection-diffusion equations.

In this paper, a rectangular lattice Boltzmann model is proposed for nonlinear convection-diffusion equations (NCDEs). The model can be used to solve NCDEs with very general form by using a real/complex-valued quadric equilibrium distribution function and relaxation time. Detailed simulations on several examples are performed to validate the model. The numerical results show good agreement with...

Finite-difference lattice Boltzmann model for nonlinear convection-diffusion equations

A lattice Boltzmann model for convection-diffusion equation with nonlinear convection and isotropic-diffusion terms is proposed through selecting equilibrium distribution function properly. The model can be applied to the common real and complex-valued nonlinear evolutionary equations, such as the nonlinear Schrödinger equation, complex Ginzburg-Landau equation, Burgers-Fisher equation, nonline...

Lattice Boltzmann-Langevin Equations

Intrinsic fluctuations around the solution of the lattice Boltzmann equation are described or modeled by addition of a white Gaussian noise source. For stationary states a fluctuation-dissipation theorem relates the variance of the fluctuations to the linearized Boltzmann collision operator and the pair correlation function.

Lattice Boltzmann Simulation of Some Nonlinear Complex Equations

In this paper, the lattice Boltzmann method for convectiondiffusion equation with source term is applied directly to solve some important nonlinear complex equations, including nonlinear Schrödinger (NLS) equation, coupled NLS equations, Klein-Gordon equation and coupled Klein-Gordon-Schrödinger equations, by using complex-valued distribution function and relaxation time. Detailed simulations o...

A Stability Notion for Lattice Boltzmann Equations