(156f) Computational-Hydrodynamic Studies of the Noh Compressible Flow Problem Using Non-Ideal Equations of State

The â??Noh problemâ? is classic verification problem in the field of computational hydrodynamics of compressible flows. A strong outward facing shockwave is created by impinging a uniformly flowing ideal gas on a hard wall (or imploding it onto the axis of a cylinder or the center of a sphere, depending on the geometry of interest). A simple problem to conceptualize and one which admits an exact analytical solution, it is nonetheless devilishly difficult for numerical codes to predict correctly, making it an ideal code-verification test bed. In its original incarnation, and in nearly all applications since, the fluid is a simple ideal gas; once validated, however, these codes are often used to study highly non-ideal fluids and solids. In this work the classic Noh problem is extended beyond the commonly-studied polytropic ideal gas to more realistic equations of state (EOS) including the stiff gas, the Nobel-Abel gas, and the Carnahan-Starling hard-sphere fluid, thus enabling verification studies to be performed on more physically-realistic fluids. Self-similarity methods are used to solve the Euler compressible flow equations, which in combination with the Rankine-Hugoniot jump conditions, provide a tractable general solution. In the planar case, this solution can be applied to any equation of state and does not necessarily have to exhibit strong shocks; for cylindrical and spherical geometries it is necessary that the analysis be restricted to strong shocks. The exact solutions are compared with numerical results obtained from the Lagrangian hydrocode FLAG, developed at Los Alamos. For these more realistic EOSs, the simulation errors decreased in magnitude both at the origin and at the shock, but also spread more broadly about these points compared to the ideal EOS. The overall spacial convergence rate remained first order. (LA-UR-16-23103)