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.