Improvement And Application Of Lattice Boltzmann Method

The lattice Boltzmann method is a mesoscopic numerical method which has themerits of the easy boundary treatment and the parallel computational ability, and itattract many scholars’ attention. However, it also has some limits. One of them is thatthe discrete velocity model with a regular shape can not be directly used into theirregular computational zone. A special one of solutions to this problem is to add asupplemented approximation process after the transformation of particles. It assumesthat the discrete velocity distribution function is continuous in space. The advantage ofthis method is that the parallel computational ability is retained and supplementedcoefficients can be computed before the whole simulation. Many supplementedapproximation formulas have been proposed before, but all of them still have somelimits.Thus the least square supplemented scheme was proposed from the analysis here.The numerical character was examined by the simulation of the bottom heating naturalconvection on the regular grids. The character and implementation details were studiedwhen this scheme was directly applied into the irregular grids by the natural convectionin the annulus between horizontal concentric cylinders. The adaptive strategy was alsostudied in this case. Then the character of heat transformation of the driven flow andhybrid convection in the polar cavity was studied by this method. The main results wereas follows:(1) The general Lagrange interpolation scheme and the least square supplementedscheme were respectively proposed. The latter one of them had the better numericalpractical character.(2) The bottom heating natural convection on the regular grids was simulated. Theresult proved that the least square supplemented scheme was feasible on the regularuniform girds.(3) The character and implementation details were devised when this scheme wasdirectly applied into the irregular grids through the natural convection in the annulusbetween horizontal concentric cylinders. The adaptive strategy was also studied in thiscase. The result indicated that the scheme still did well in some range of the irregulardistribution of nodes.(4) The driven flow and hybrid convection in the polar cavity were simulated by this method. The character of heat transformation was studied. The result indicated thatthe least square supplemented scheme was general in different physical problems.