比例边界坐标插值方法在谱元法中的应用——无穷域Euler方程的数值模拟

将比例边界坐标插值方法引入谱元法, 构成比例边界谱单元, 对无穷域Euler方程进行数值模拟.阐述了比例边界谱单元的基本使用方法以及基于比例边界谱元的Runge-Kutta间断Galerkin方法求解Euler方程的过程;计算了无穷域圆柱和NACA0012翼型绕流问题, 并与已有结果进行了比较, 显示了计算结果的正确性.用基于比例边界谱元的间断Galerkin方法求解无穷域Euler方程时, 最多只需将求解域划分为2个子域, 避免了一般谱方法将求解域划分为9个或者27个子域的麻烦. 比例边界谱单元为无穷域Euler方程的直接求解提供了一个可供参考的方法.

THE SCALED BOUNDARY COORDINATE INTERPOLATION METHOD AND ITS APPLICATION TO SPECTRAL ELEMENT METHOD: NUMERICAL SIMULATION OF THE EULER EQUATIONS OVER UNBOUNDED DOMAINS

A new infinite element,by combining the scaled boundary coordinate interpolation method and spectral element method, named scaled boundary spectral element (SBSE), to solve Euler equations over infinite domains directly is presented in this paper. The usage of SBSE and the procedures for solving Euler equations using Runge-Kutta discontinuous Galerkin (RKDG) method are described. Two typical subsonic flow cases, around a circular cylinder and around NACA0012 airfoil, are simulated, which illustrate the correctness of this method. When one solve Euler equations over infinite domains directly with SBSE, the solution domain need be divided into 2 sub-domains at most, avoiding the trouble of dividing the solution domain into 9 or 27 sub-domains when one do the same thing with spectrum methods. The numerical results demonstrate that SBSE provides an available choice for solving Euler equations over infinite domains directly.