Applied Mathematics and Computation
Nonlinear Stability of Compressible Thermal Lattice BGK Models
SIAM Journal on Scientific Computing
A Lattice Boltzmann equation for waves
Journal of Computational Physics
On the long-time behaviour of soliton ensembles
Mathematics and Computers in Simulation - Nonlinear waves: computation and theory II
Three-dimensional multi-relaxation time (MRT) lattice-Boltzmann models for multiphase flow
Journal of Computational Physics
A steady-state lattice Boltzmann model for incompressible flows
Computers & Mathematics with Applications
Lattice Boltzmann model for elastic thin plate with small deflection
Computers & Mathematics with Applications
A Lattice Boltzmann Model for the Reaction-Diffusion Equations with Higher-Order Accuracy
Journal of Scientific Computing
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In this paper, a lattice Boltzmann model for the Korteweg-de Vries (KdV) equation with higher-order accuracy of truncation error is presented by using the higher-order moment method. In contrast to the previous lattice Boltzmann model, our method has a wide flexibility to select equilibrium distribution function. The higher-order moment method bases on so-called a series of lattice Boltzmann equation obtained by using multi-scale technique and Chapman-Enskog expansion. We can also control the stability of the scheme by modulating some special moments to design the dispersion term and the dissipation term. The numerical example shows the higher-order moment method can be used to raise the accuracy of truncation error of the lattice Boltzmann scheme.