Linearization for the Boltzmann equation

Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation

Xiaoyi He1,2,* and Li-Shi Luo Center for Nonlinear Studies, MS-B258, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 Complex Systems Group T-13, MS-B213, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 ICASE, MS 403, NASA Langley Research Center, 6 North Dryden Street, Building 1298, Hampton, Virginia 23681-0001 ~Received 29 April 1997; revised ma...

Solving the Boltzmann Equation

In [32, 31], fast deterministic algorithms based on spectral methods were derived for the Boltzmann collision operator for a class of interactions including the hard spheres model in dimension 3. These algorithms are implemented for the solution of the Boltzmann equation in dimension 2 and 3, first for homogeneous solutions, then for general non homogeneous solutions. The results are compared t...

Local Hilbert Expansion for the Boltzmann Equation

We revisit the classical work of Caflisch [C] for compressible Euler limit of the Boltzmann equation. By using a new L2-L∞ method, we prove the validity of the Hilbert expansion before shock formathions in the Euler system with moderate temperature variation.

Stochastic numerics for the Boltzmann equation

discuss its properties and briefly describe the Direct Simulation Monte Carlo (DSMC) method (see [1]) which is widely applied in numerics. Then, in the second part of the talk, we present the Stochastic Weighted Particle Method (SWPM) which was introduced in [2]. This numerical method was developed for problems with big deviation in magnitude of values of interest. We describe the corresponding...

Implicit Schemes for the Lattice Boltzmann Equation