Simulations of the Experiments Ken Powell CRASH Review October, 2010

CRASH Preprocessor Hyades is a Lagrangian rad-hydro code that can model laser-plasma interactions Used in the early stage (first 1.1 ns) of the simulations Map Hyades Lagrangian result to CRASH Eulerian grid, via triangulation and interpolation Ongoing work to build our own laser package (see Igor Sokolov’s talk) Have also experimented with X-ray-driven initialization by CRASH or Hyades (See Eric Myra’s and Erica Rutter’s posters)

CRASH Radhydro Code: Hydro and Electron Physics radiation/electron momentum exchange radiation/electron energy exchange electron heat conduction Compression work collisional exchange

CRASH Radhydro Code: Multigroup diffusion Radiation transport equation reduces to a system of equations for spectral energy density of groups. Diffusion is flux-limited For the g th group: advectioncompression workphoton energy shift

Overview of Solver Approach Self-similar block-based adaptive grid Finite-volume scheme, approximate Riemann solver for flux function, limited linear interpolation Level-set equations used to evolve material interfaces; each cell treated as single-material cell Mixed Implicit/Explicit update o Hydro and electron equations  Advection, compression and pressure force updated explicitly  Exchange terms and electron heat conduction treated implicitly o Radtran  Advection of radiation energy, compression work and photon shift are evaluated explicitly  Diffusion and emission-absorption are evaluated implicitly o Implicit scheme is a block-ILU-preconditioned Newton-Krylov- Schwarz scheme

CRASH Postprocessor Synthetic radiographs generated by integrating absorption coefficients along lines of sight Poisson noise is added to simulate finite photon count Smoothing is done at scale associated with finite aperture in experiment Tests included in verification suite – grid-convergence studies on problems with analytical solutions

Improvements to fidelity/efficiency finished this year Electron/radiation physics o Flux limiting added - limit Spitzer-Harm flux by fraction of free-streaming heat flux o Update based on total energy, but slope limiter applied on primitive variables EOS and opacity calculations o Five material (Xe, Be, Au, acrylic, polyimide) EOS and opacity tables in place o EOS tables made reversible (E→p→E or p→E→p puts you back where you started) Efficiency improvements o New block-adaptive-tree library (BATL); Efficient dynamic AMR in 1, 2 and 3D o Semi-implicit scheme, split by energy group  Requires less memory and CPU. Allows PCG. Synthetic radiographs with blurring o Add Poisson noise due to finite photon count. o Smooth at the scale that corresponds to the pinhole size.

Pure Hydro Results 3 geometries o Straight tube (1200 μm diameter) o Step (1200 μm → 600 μm) o Nozzle (1200 μm → 600 μm) 250 μm Be disk, low laser energy Shock speed ~ 20 km/s Highest 3D resolution to date o 2 μm spacing o 2400 x 480 x 480 uniform grid o 550 million cells

Pure Hydro Results – Density Contours Nozzle – Vertical cutNozzle – Horizontal cut Step – Vertical cut Step – Horizontal cut

Pure Hydro Results – Resolution Effects 1 μm TubeNozzle 2 μm 4 μm 8 μm

Full Physics Results 2 geometries o 2D Straight tube (600 μm) o 3D Nozzle (1200 μm → 600 μm) 20 μm Be disk, nominal laser energy (3.8 kJ for 1 ns) Shock speed ~ 160 km/s Electron physics, five materials, 30 energy groups Varying resolutions o 2D - 2 μm effective (1 AMR level) o 2D μm effective (3 AMR levels) o 3D - 4 μm effective (1 AMR level, 5 million cells)

2D Results – 2 μm Resolution

2D Results – 0.5 μm Resolution

3D Results – Elliptical 4 μm Resolution

Ongoing Challenge – Morphology Conundrum

The morphology conundrum persists independent of: Mesh resolution (except on very coarse grids) Flux function, limiter Gray vs multigroup/number of groups Treatment of electron physics Number of materials used Presence or absence of a symmetry axis

We CAN make a primary shock with realistic structure with different initial conditions (X-ray-driven) running CRASH alone But it is hard to get the primary shock and the wall ablation to simultaneously match the experimental result…

… and we get different results when initializing the same case using Hyades Hyades-driven X-Ray case CRASH-driven X-Ray case

The path ahead We are further pursuing the X-ray-driven case, comparing Hyades and CRASH to understand how the differences arise We are developing a laser package, so we have an alternative preprocessor, one whose internal working we understand/have control over We are working to improve the preconditioning of the implicit solve, to cut down the compute time (approximately 90% of compute time is spent here)