Source: https://verification.asmedigitalcollection.asme.org/article.aspx?articleid=2730434
Timestamp: 2019-04-19 07:01:14+00:00

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Manuscript received December 21, 2018; final manuscript received March 27, 2019; published online April 16, 2019. Assoc. Editor: Kyle Daun. The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States government purposes.
Los Alamos National Laboratory is interested in developing high-energy-density physics validation capabilities for its multiphysics code xRAGE. xRAGE was recently updated with the laser package Mazinisin to improve predictability. We assess the current implementation and coupling of the laser package via validation of laser-driven, direct-drive spherical capsule experiments from the Omega laser facility. The ASME V&V 20-2009 standard is used to determine the model confidence of xRAGE, and considerations for high-energy-density physics are identified. With current modeling capabilities in xRAGE, the model confidence is overwhelmed by significant systematic errors from the experiment or model. Validation evidence suggests cross-beam energy transfer as a dominant source of the systematic error.
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Early implosion dynamics of a typical ICF validation experiment. First, significant energy from high energy lasers is absorbed into the capsule ablator shell via inverse bremsstrahlung. Next, the outer shell ablation accelerates the shell inward and compresses the fuel and inner layers to very high temperatures and pressures: 1–plasma formation and 2–ablative compression.
Electron temperature and density profiles at 1800 ps (top), 2200 ps (middle), and 2600 ps (bottom) during the drive for the high energy Be ablator shells. Ablation front is indicated by vertical dashed line. As time progresses, a dense plasma separates the ablation front from the bulk mass.
Example of the experimental data for the Be (high) case. QoI shown are the laser energy (), scattered energy (), absorbed energy (), ablation front position (), and ablation front velocity (). Uncertainties are on the order of symbol size.
The initial mesh (top) and geometry (bottom) given to xRAGE. To better show the capsule geometry, the geometry scale is exaggerated. Mesh spacing is realistic.
Numerical uncertainty assessment of the (a) scattered laser energy and (b) ablation front position. Estimated numerical error ẽN,ϕ of the nominal grid size (blue) is contained within the GCI-estimated standard numerical uncertainty (shaded gray region). The scattered energy and ablation front QoI with numerical uncertainty (green shaded regions) are shown as a reference. The numerical error L1 norm shown on the right with reference convergence rates of one-half, one, and two: (a) ϕps(TW) and (b) ϕr (μm).
Contributions of input parameters (i.e., mass ma, incident laser power Pi, density ρa, beam radius rbeam, and capsule radius ro) to the total validation uncertainty uV,ϕ for the C high case. Input parameters with negligible influence (e.g., inner and outer gas pressures and densities) are not shown: (a) ϕps(TW) and (b) ϕr (μm), and (c) ϕυ (km/s).
Validation assessment of QoI (top) and model error normalized by model requirements (bottom) for the nominal case. Comparison of scattered laser light (green), shell trajectories (red), and shell velocities (cyan) for experimental data (symbols)  and xRAGE (lines). Validation uncertainty (i.e., 1σ, 2σ, and 3σ confidence) given as shaded regions. Incident laser power (black) is shown as a reference: (a) C (l), (b) C (h), (c) Be (l), and (d) Be (h).
Sensitivity to the laser energy deposited during the first laser picket (i.e., 1.5 Pi,t≤0.3 (—), Pi (— —), and 0.5Pi,t≤0.3 (— –), respectively. Comparison of laser power (black), scattered laser energy (green), and shell trajectory (red). The results are presented for the C ablator shell at high laser power. Incident laser power (black) is shown as a reference.
Sensitivity to the flux limiter and identification of the flux limiter-independent value (i.e., nonlocal Schurtz model (—) and local Spitzer models with f = 0.03 (— —), f = 0.05 (— — –), and f = 0.15 (— –), respectively. Comparison of scattered laser energy (green) and shell trajectory (red). The results are presented for the C ablator shell at high laser power. Incident laser power (black) is shown as a reference. For plot clarity, f = 0.04, 0.07, and 0.10 are not shown.
Validation assessment of QoI (top) and model error normalized by model requirements (bottom) for the flux limiting case. Comparison of scattered laser energy (green), shell trajectories (red), and shell velocities (cyan) for experimental data (symbols)  and xRAGE (lines). Validation uncertainty (i.e., 1σ, 2σ, and 3σ confidence) given as shaded regions. Incident laser power (black) is shown as a reference: (a) C (h)—flux limiting, (b) Be (h)—flux limiting.
Validation assessment of QoI (top) and model error normalized by model requirements (bottom) for the laser scaling case. Comparison of scattered laser energy (green), shell trajectories (red), and shell velocities (cyan) for experimental data (symbols)  and xRAGE (lines). Validation uncertainty (i.e., 1σ, 2σ, and 3σ confidence) given as shaded regions. Incident laser power (black) is shown as a reference: (a) C (h)—laser scaling and (b) Be (h)—laser scaling.
Wilson BM, Koskelo A. Assessment of Model Confidence of a Laser Source Model in xRAGE Using Omega Direct-Drive Implosion Experiments. ASME. J. Verif. Valid. Uncert. 2019;3(4):041003-041003-12. doi:10.1115/1.4043370.
Grid-Induced Numerical Errors for Shear Stresses and Essential Flow Variables in a Ventricular Assist Device: Crucial for Blood Damage Prediction?

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