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

Authors:
Y. Bazilevs;C. C. Long;I. Akkerman;D. J. Benson;M. J. Shashkov
Affiliations:
Department of Structural Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92123, USA;T-3 Fluid Dynamics and Structural Mechanics, Los Alamos National Laboratory, Los Alamos, NM 87545, USA;School of Engineering and Computing Sciences, Durham University, Science Site, South Rd., Durham, DH1 3LE, United Kingdom;Department of Structural Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92123, USA;XCP-4 Methods and Algorithms, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Venue:
Journal of Computational Physics
Year:
2014

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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.