Symmetry-preserving WENO limiters

Abstract

Weighted essentially non-oscillatory (WENO) reconstruction schemes are presented that preserve cylindrical symmetry for radial flows on an equal-angle polar mesh. These new WENO schemes are used with a Lagrangian discontinuous Galerkin (DG) hydrodynamic method. The solution polynomials are reconstructed using the WENO schemes where the DG solution is the central stencil. A suite of challenging test problems are calculated to demonstrate the accuracy and robustness of the new WENO schemes.