Isogeometric analysis of Lagrangian hydrodynamics: Axisymmetric formulation in the rz-cylindrical coordinates

Abstract

A recent Isogeometric Analysis (IGA) formulation of Lagrangian shock hydrodynamics [4] is extended to the 3D axisymmetric case. The Euler equations of compressible hydrodynamics are formulated using the rz-cylindrical coordinates, and are discretized in the weak form using NURBS-based IGA. Artificial shock viscosity and internal energy projection are added to stabilize the formulation. The resulting discretization exhibits good accuracy and robustness properties. It also gives exact symmetry preservation on the appropriately constructed meshes. Several benchmark examples are computed to examine the performance of the proposed formulation.