LHD国际学术报告会

报告题目： Lattice Boltzmann Method versus Artificial Compressibility Method

报告人：Prof. T. Ohwada, Kyoto University

报告时间：2010年8月27日周五上午10：00

报告地点：力学所主楼312会议室

报告摘要：

The lattice Boltzmann method (LBM) has a close analogy with the artificial compressibility method (ACM) for the incompressible Navier-Stokes equations. The asymptotic analysis of the LBM updating rule derives the equation system of ACM, which consists of the continuity equation with the pressure time derivative multiplied by the Mach number squared and the usual momentum equation in the NS equation system. This equation system yields the solution of the incompressible Navier-Stokes system in the limit of vanishing Mach number. For this reason, LBM can be regarded as a kinetic ACM. The superiority of LBM over ACM is widely believed, which is seen, for example, from the fact that more than 3000 LBM papers have been published while only about 300 ACM papers have appeared so far and the statement in the paper by He, Doolen, and Clark [JCP2002] ``the lattice Boltzmann method starts with the kinetic theory and has been derived to conserve high-order isotropy, the lattice Boltzmann method {\it should be} more accurate than the artificial compressibility method." Nevertheless, the clear demonstration or the decisive evidence has not yet been reported so far. In this talk, we will first explain about the improvement of ACM, such as Richardson's extrapolation in the Mach number, which brings drastic gain in the accuracy, the suppression of checkerboard instability, and the enhancer of the stability. Then we will discuss the similarity and the difference between LBM and the fortified ACM on the basis of the theoretical consideration and some numerical results. The discussion will suggest the necessity of the modification of the folk belief about the superiority of LBM.