A thermodynamic lattice Boltzmann model whose equilibrium distribution function include high order terms of velocity and internal energy terms is presented, and a new kind of implement of gravity and temperature boundary is also proposed by which thermodynamics phenomenon permits to be simulated. Based on the HPP model, a three-overlapped HPP lattice Boltzmann model is introduced. The Benard pattern of thermal convection phenomenon has been simulated successfully by using this model on SUN workstation computer.

A parallel computational model of simulating hydrodynamic phenomena is introduced. This model is used to simulate Karman votices streets. By using the computer visualization technique, it can automatically and dynamically demonstrate the evolving process of fluid flow, and easily analyse the variety of hydrodynamic phenomena.

Lattice method is a new method of numerical simulation for fluid dynamics developed recently.Its essential idea is the model-rebuilding.Based on this method two models are composed for linear and quasi-linear parabolic equations.Several typical numerical examples are studied using the models and satisfactory results are achieved.