AUFS格式在无网格方法中的应用

将计算量小，激波分辨率高的AUFS (artificially upstream flux vector splitting) 格式应用于无网格方法. 所发展算法基于多项式基函数最小二乘无网格方法，采用线性基函数曲面拟合及AUFS 格式计算各离散点的空间导数，应用四阶Runge-Kutta 法进行时间显式推进. 为验证算法健壮性、精度以及计算效率，对Riemann 问题、超音速平面流动，以及不同攻角NACA0012 翼型跨音速流场进行了数值模拟，其结果同采用HLLC (Harten-Lax-van Leer-contact) 格式的无网格方法以及文献报道结果吻合较好，并且计算量较形式简单HLLC 格式减少约15%.

APPLICATION OF AUFS SCHEME IN GRIDLESS METHOD

The artificially upstream flux vector splitting (AUFS) scheme is extended into a gridless method successfully. This gridless method is based on the polynomial basis least-squares method, the curve fitting of linear basis function and AUFS scheme are employed to calculate the spatial derivatives, and a four-stage Runge-Kutta algorithm is applied to advance the Euler equations in time. In order to demonstrate the effciency and the accuracy of this method, a Riemann problem, a supersonic flow in channel, and a transonic flow of NACA0012 airfoil at di?erent attack angles are simulated, and the results are in good agreement with the results calculated by the HLLC (Harten-Lax-van Leer-contact) scheme and other references. Besides, the time spent in the AUFS scheme is about 15% less than in the HLLC scheme.