A Computational Biofluid Dynamic Approach Using The General Lattice Boltzmann Equation.

Abstract

The lattice Boltzmann method (LBM) is a modern numerical technique, very
efficient, flexible to simulate different flows within complex/varying geometries. The LBM has
evolved from the lattice gas automata (LGA) in order to overcome the difficulties with the
LGA. The core equation in the LBM turns out to be a special discrete form of the continuum
Boltzmann equation, leading it to be self-explanatory in statistical physics. In contrast with
the traditional computational fluid dynamics (CFD) based on a direct solution of flow
equations, the lattice Boltzmann method provides an indirect way for solution of the flow
equations. This method is characterized by simple calculation, parallel process and easy
implementation of boundary conditions. This feature makes the lattice Boltzmann method a
very promising computational approach in different areas. A computational code is described
for numeric simulations of blood flow using the Cellular Automata theory, applying the lattice
Boltzmann general equation (GLBE). The algorithm and user's environment are also
described. The mathematical theory required for the program code is also included and a
formal example is included to show the versatility and power of the method.