In 1917, the British scientist LF Richardson made the first reported attempt to predict the
weather by solving partial differential equations numerically, by hand! It is generally …

In recent years, stylized forms of the Boltzmann equation, now going by the name of" Lattice
Boltzmann equation"(LBE), have emerged, which relinquish most mathematical complexities …

In this paper, the lattice Boltzmann equation is directly derived from the Boltzmann equation.
It is shown that the lattice Boltzmann equation is a special discretized form of the Boltzmann …

This paper presents an improved gas-kinetic scheme based on the Bhatnagar–Gross–Krook
(BGK) model for the compressible Navier–Stokes equations. The current method extends …

Smooth particle hydrodynamics (SPH) is usually based on equations derived from the
momentum and thermal energy equations of fluid dynamics. Artificial viscosity is added to …

This paper examines the use of computational fluid dynamics as a tool for aircraft design. It
addresses the requirements for effective industrial use, and trade-offs between modeling …

Computational fluid dynamics (CFD) studies the flow motion in a discretized space. Its basic
scale resolved is the mesh size and time step. The CFD algorithm can be constructed …

The lattice Boltzmann method (LBM) is regarded as a specific finite difference discretization
for the kinetic equation of the discrete velocity distribution function. We argue that for finite …

A new high-resolution and genuinely multidimensional numerical method for solving
conservation laws is being developed. It was designed to avoid the limitations of the …

With discretized particle velocity space, a multi-scale unified gas-kinetic scheme for entire
Knudsen number flows has been constructed based on the kinetic model in one …