AUFS格式在无网格方法中的应用

APPLICATION OF AUFS SCHEME IN GRIDLESS METHOD

  • 摘要: 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%.

     

    Abstract: 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.

     

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