Title: Advances in node-centered Lagrangian shock hydrodynamics on brick- and simplex-type finite elements (2009 CSRI Summer Lecture Series)

Speaker: Guglielmo Scovazzi, Sandia National Laboratories

Date/Time: Wednesday, July 22, 2009, 3-4pm (MST)     

Location: CSRI Building, Room 90 (NM), 915/S145 (CA)

Brief Abstract: Hydrocodes - or algorithms for shock hydrodynamics computations - have a long history, initiated in the years of the Manhattan Project at Los Alamos National Laboratories. Over the years, they evolved from simple one-dimensional schemes to fully three-dimensional production software. Hydrocodes are used to compute highly transient phenomena, such as blasts, explosions, impacts, and their use is widespread not only in the National Laboratories, but also in industry. Typical applications include: Design of conventional and nuclear weapons, design of high energy density systems (Z- pinch, NIF, etc.), design and analysis of armored systems, meteorite impact analysis, supernovae simulations, crash worthiness analysis of aircrafts, spacecrafts, cars, trains, buildings, etc.
  
The first part of the lecture will review the main historical milestones in the development of hydrocodes and the main issues and open questions in the advancement of their technology. Then, a new, variational multiscale stabilized formulation for Lagrangian shock will be presented [1, 2, 3].
  
To the author’s knowledge, it is the only hydocode that can accurately compute highly unsteady shock hydrodynamics transients on triangular/tetrahedral meshes in two/three dimensions, as well as the more commonly used quadrilateral/hexahedral meshes. The proposed method leverages a quasi-linear formulation of the Lagrangian shock hydrodynamics equations, and global conservation is attained with an approach that differs from most of the stabilized methods for compressible flows. Piecewise linear, equal-order interpolation for velocities, displacements, and thermodynamic variables (specifically pressure or internal energy, depending on the preferred formulation) is adopted. This last aspect makes the current formulation insensitive to the typical pathologies affecting standard hydrocodes (namely hourglass on quadrilat- eral/hexahedral meshes, and artificial stiffness on triangular/tetrahedral meshes). The stabilization involves additional design requirements [4, 5] with respect to the corre- sponding operators found in the literature for compressible aerodynamics applications, due to the highly unsteady nature of the problems to be solved, which may include blast/implosions. Numerical tests for the unsteady Euler equations of gas dynamics are presented in two and three dimensions.

References
 [1] G. Scovazzi. Stabilized shock hydrodynamics: III. A new stabilization concept for Lagrangian Computations. Computer Methods in Applied Mechanics and Engineering, 2009. Submitted.
 [2] G. Scovazzi, J. N. Shadid, E. Love, and T. J. R. Hughes. Stabilized shock hydro-dynamics: IV. Computations with a conservative updated Lagrangian method. Computer Methods in Applied Mechanics and Engineering, 2009. Submitted.
[3] G. Scovazzi, W. J. Rider, E. Love, and J. N. Shadid. Stabilized shock hydrodynamics: V. Von Neumann stability analysis of a predictor/multi-corrector Lagrangian method. Computer Methods in Applied Mechanics and Engineering, 2009. Submitted.
[4] G. Scovazzi. A discourse on Galilean invariance and SUPG-type stabilization. Computer Methods in Applied Mechanics and Engineering, 196(4–6):1108–1132, 2007.
[5] G. Scovazzi. Galilean invariance and stabilized methods for compressible flows.
International Journal for Numerical Methods in Fluids, 54(6–8):757–778, 2007.

CSRI POC: Zhaofang Wen, (505) 284-0206