求解Euler方程的无网格与有限体积混合算法研究

研究了无网格方法与有限体积法相结合的、求解Euler方程的混合算法.与单一的无网格方法相比较,由于在大部分计算区域采用了有限体积法,使得发展的算法在运算效率上能与有限体积法相当;同时在物体附近嵌入了无网格区,使得在处理几何外形上更具灵活性.有关算法涉及的无网格与网格区域搭接处理,通过在交界面处引入辅助卫星点和网格单元构成边界信息,实现了区域间的流动信息传递.Euler方程的空间导数分别在两区域用有限体积法和无网格法离散近似,时间方向都采用四步显式Runge-Kutta格式推进求解,数值模拟了喷管内流和绕翼型外流,并分别与整体有限体积法和整体无网格方法进行了比较.算例展示出,提出的混合算法能有效捕捉激波间断,且两区域等值线过渡光滑,算法效率如预期与有限体积法相当,表明该方法是可行的.

A Gridless-Finite Volume Hybrid Algorithm for Euler Equations

A fast hybrid algorithm based on gridless method coupled with finite volume method (FVM) is de- veloped for the solution to Euler equations. Compared with pure gridless method, the efficiency of the hybrid algorithm is improved to the level of finite volume method for most parts of the flow filed are covered with grid cells. Moreover, the hybrid method is flexible to deal with the configurations as clouds of points are used to cover the region adjacent to the bodies. Mirror satellites and mirror grid cells are introduced to the interface to accomplish data communication between the different parts of the flow field. The Euler Equations are spatially discretized with finite volume method and gridless method in mesh and clouds of points respectively, and an explicit four-stage Runge-Kutta scheme is utilized to reach the steady-state solution. Internal flows in channels and external flows over airfoils are investigated with hybrid method, and the solutions are compared to those using pure finite volume method and pure gridless method. Numerical examples show that the hybrid algorithm captures the shock waves accurately, and it is as efficient as finite volume method.