User:
Lattice Boltzmann Method
Description
The problem with macro scale systems that are based on microscopic phenomena is that
- macroscopic models are too simple to correctly reflect the dynamics
- microscopic models to describe the macroscopic reality can not be solved analytically and numerical solutions are cumbersome (= require a lot of computational resources)
The Boltzmann lattice method looks for an intermediate path. It is based on the Boltzmann transport equation, rescues the microscopic part via the collision term and implements a simplified structure to calculate the macroscopic results. We speak of a mesoscopic approach where we can, as required, reduce microscopic effort by losing accuracy but saving resources or improving accuracy by investing more resources.
ID:(8488, 0)
Distributions in Position and Moment
Description
The distribution function must consider all the particles, both primary and secondary. It should reflect the fact that these are appearing or can be reduced in time.
For each cell in space must include the energy distribution and direction in which it travels. This should be done with the proper description of both the spatial variables (cells) and the space of moments.
ID:(9149, 0)
Introduction of Distributions
Description
The main problem of the Monte Carlo Method lies in the need to combine all possible alternatives giving a high number of combinations.
A second approach is to transform the detailed information generated in a Monte Carlo model into its distributions and solve the corresponding associated transport equations.
The distribution functions also require the introduction of a grid or cell structure that allows to describe the particles present in it.
ID:(9148, 0)