Abstract
WENO (Weighted essentially non-oscillatory)-type reconstruction schemes are used to work as a limiter that preserves cylindrical symmetry for radial shock flows on an equal-angle polar mesh in Lagrangian hydrodynamics. These WENO-type limiters are tested with a high-order Lagrangian discontinuous Galerkin (DG) hydrodynamic method. In order to guarantee the compactness of the underlying DG methods, for strong shock problems, canonical WENO and Hermite WENO reconstructions are used for second-order DG(P1) and third-order DG(P2) respectively, using the known DG solution for the target cell as the central stencil. A salient feature of Hermite WENO lies in taking advantage of available information, namely the derivatives that are evolved with the DG method. With a local orthonormal basis or a local characteristic decomposition, the WENO-type reconstruction schemes can guarantee the cylindrical symmetry for Lagrangian hydrodynamics. A suite of challenging test problems are calculated to demonstrate the accuracy and robustness of these WENO-type schemes.
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