A cylindrical discontinuous Galerkin method for compressible flows in axisymmetric geometry

In this paper, we present a cylindrical discontinuous Galerkin method for compressible flows in axisymmetric geometry. The axisymmetric Euler equations in geometric flux form are discretized by the Runge-Kutta DG method. To ensure conservativeness when using limiters developed for the 1-and 2-dimensional planar problems, the basis is modified from the Legendre polynomials such that the non-zero order moments in each cell do not contribute to the cell average value. Several 1-and 2-dimensional cylindrical tests are implemented and compared with the reference results. The present method exhibits the expected order accuracy in smooth problems and has a good performance in some challenging tests such as Noh problem and Sedov problem.