Application of the Noh Problem to Al, Fe, W, Cu

Verification problems test a computer codeâ??s ability to numerically solve a problem with a known exact solution. This is useful because by correctly solving a problem with a known solution, it increases our confidence that it can solve more complex problems for which the solutions are unknown. Here we revisit the Noh verification test problem. The one-dimensional planar Noh problem is comprised of a compressible, ideal gas of negligible viscosity that is initialized with a uniform, inward velocity, impinging on a hard wall. This flow pattern creates an outgoing shock wave at the origin, and is commonly used to assess a codeâ??s ability to convert kinetic energy into internal energy. These characteristics of the Noh problem make it simple, analytically; yet it remains a very difficult numerical problem. Traditionally, the Noh problem is run using an ideal gas. Recently, however, Burnett et al, have shown that an analytical solution may also be obtained with the â??stiff gasâ? equation of state. The stiff gas is relatively simple in form but gives a qualitatively accurate representation of many metals, while allowing condensed-phase materials to go both into compression and tension. Here we implement the stiff-gas EOS in the Noh problem to model the behavior of aluminum, copper, iron and tungsten under shocked or extreme conditions and evaluate the codeâ??s ability to follow the thermodynamic behavior of the material. These hydrodynamic verification studies were done using the LANL Eulerian code xRAGE and the LANL Lagrangian code FLAG. Numerical results are compared to the exact stiff-gas results and to the experimental shock Hugoniot, and mesh convergence studies are performed. Our results show that this classic and widely-studied verification test problem can be extended beyond the ideal gas to physically realistic materials of practical interest