Abstract
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.
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