Thomas Masser

Cross-code comparisons of mixing during the implosion of dense cylindrical and spherical shells

We present simulations of the implosion of a dense shell in two-dimensional (2D) spherical and cylindrical geometry performed with four different compressible, Eulerian codes: RAGE, FLASH, CASTRO, and PPM. We follow the growth of instabilities on the inner face of the dense shell. Three codes employed Cartesian grid geometry, and one (FLASH) employed polar grid geometry. While the codes are similar, they employ different advection algorithms, limiters, adaptive mesh refinement (AMR) schemes, and interface-preservation techniques. We find that the growth rate of the instability is largely insensitive to the choice of grid geometry or other implementation details specific to an individual code, provided the grid resolution is sufficiently fine. Overall, all simulations from different codes compare very well on the fine grids for which we tested them, though they show slight differences in small-scale mixing. Simulations produced by codes that explicitly limit numerical diffusion show a smaller amount of small-scale mixing than codes that do not. This difference is most prominent for low-mode perturbations where little instability finger interaction takes place, and less prominent for high- or multi-mode simulations where a great deal of interaction takes place, though it is still present. We present RAGE and FLASH simulations to quantify the initial perturbation amplitude to wavelength ratio at which metrics of mixing agree across codes, and find that bubble/spike amplitudes are converged for low-mode and high-mode simulations in which the perturbation amplitude is more than 1% and 5% of the wavelength of the perturbation, respectively. Other metrics of small-scale mixing depend on details of multi-fluid advection and do not converge between codes for the resolutions that were accessible.

The Sedov Test Problem

The Sedov test is classically defined as a point blast problem. The Sedov problem has led us to advances in algorithms and in their understanding. Vorticity generation can be physical or numerical. Both play a role in Sedov calculations. The RAGE code (Eulerian) resolves the shock well, but produces vorticity. The source definition matters. For the FLAG code (Lagrange), CCH is superior to SGH by avoiding spurious vorticity generation. FLAG SGH currently has a number of options that improve results over traditional settings. Vorticity production, not shock capture, has driven the Sedov work. We are pursuing treatments with respect to the hydro discretization as well as to artificial viscosity.

Uncertainty Models for Strong Shock Imploding Richtmyer- Meshkov Instability

[Abstract] We present a computational and uncertainty quantification study of cylindrically imploding Richtmyer-Meshkov instability. Our goal is twofold, to study the effect of solution algorithm on the dynamics of high energy flow, and to conduction a code verification study of solution error and grid convergence, including a detailed comparison between two different solution methodologies.