中文摘要：

为克服动能BGK格式计算耗时多、收敛慢的缺点，在格式中引入当地时间步长、隐式LU-SGS方法和多重网格技术，基于RAE2822翼型粘性跨声速绕流的数值模拟，对其收敛性的改善进行了研究。结果表明：上述3种加速手段对求解定常问题时的收敛性有明显的改善，达到定常解所需的迭代步数随着CFL数的提高而减少；因而求解某类问题时，隐式格式比显式格式更具优势；多重网格既适用于显式格式，也适用于隐式格式，加速性更加突出。

英文摘要：

In order to overcome the obvious drawback of gas-kinetic BGK scheme with its weak computational efficiency, three main convergence acceleration techniques, including local time stepping, implicit LUSGS method and multigrid, were adopted and tested. Based on simulation of viscous transonic steady flows over RAE2822 airfoil, their effectiveness was analyzed in detail. The following are the key results： 1. the speed-up to steady state is significant after acceleration techniques were employed; 2. as CFL number increased, needed steps for convergence is decreased; 3. multigrid is a very powerful tool and can be implemented for both explicit and implicit time-advancing methods. In this communication, the efficiency of 4-level Vcycle multigrid is the best one and its ratio of speed-up can reach 11 for explicit approach and nearly 9 for implicit scheme.