Lattice Boltzmann method is used to simulate natural convection in a cavity fill with porous medium under REV scale. Effects of Rayleigh number, Darcy number and porosity on heat transfer and flow in a square enclosure were studied. It is found that Darcy number has a great influence on fluid flow pattern in the cavity. Increasing Rayleigh number,Darcy number, and porosity enhance the heat dissipation effect. Effect of porosity on average Nusselt number is related to Darcy number. As Darcy number is small, porosity has little effect on average Nusselt number. As Darcy number is great, porosity has a great influence on average Nusselt number. As cold source is placed above the wall, average Nusselt number changes dramatically with the increase of Rayleigh number. Under high Rayleigh number condition, cooling effect is improved by arranging the cold source above the boundory.Among the six schemes, Case 6 has the best heat dissipation effect.

Kelvin-Helmholtz instability of two-dimensional immiscible incompressible fluid in a sloping tube was numerically simulated with front tracking method. Effects of inclined angles of wall, thickness of velocity gradient layer and Richardson number on development of K-H instability were investigated. It shows that the greater the angle of wall inclination is, the faster the K-H instability develops and the more liquid is rolled up. It was also found that increase of thickness of the velocity gradient layer under the inclined wall presented an inhibitory effect on roll-up of the interface. The greater gravity items of Richardson number is, the slower the interface rolls up. However, surface tension items of Richardson number have weak effect on the growth of interface.