Lawrence Livermore National Laboratory



Robert Nourgaliev

Overview

This project focuses on a scoping study and the earlier development of numerical methods for predictive simulations of the potential lethality and vulnerability of laser directed energy (DE). This requires the development of high-order implicit solvers to enable coupled fluid dynamics and thermal-structural response (solid mechanics) in a wide range of flow conditions, from low Mach to supersonic shock dynamics. The solvers must be capable of capturing relatively long-time-scale dynamics (laser DE long-time target engagement). This implicit fluid–structure interaction (FSI) capability can be used to explore local damage behavior with full system response. The project explored the recently developed reconstructed discontinuous Galerkin (rDG) method for high-order finite-element space discretization, embedded into the fully-implicit method-of-lines time discretization and the Newton–Krylov framework for solving generic conservation laws—representing a Navier–Stokes formulation for fluids and implicit solid mechanics (hydrodynamics with strength)—within the a multiphysics simulation platform. The project formulated the algorithmic and physics modeling directions needed for robust, effective, and accurate representation of the complex physics involved. The research significantly advances the general field of computational modeling in fluid–structure interactions and national-security applications by employing state-of-the-art high-fidelity portable and scalable algorithms for high-performance computing and fully coupled physics.



Figure 1.
New development and sufficiently-in-depth exploration items are highlighted in bold, while the remaining issues (deemed necessary but not investigated to the same level) are shown in gray.

Background and Research Objectives

Many science, engineering, and potential offense and defense applications require accurate simulations of the system response and fluid-structure interactions from a laser DE encounter. Since the timescale of the laser target engagement is relatively long, the modeling approach requires an implicit formulation. Numerical algorithms with explicit time stepping result in unacceptably small time steps, owing to numerical stability restrictions, which is especially detrimental when an accurate resolution of the thermal and viscous boundary layers is required in the neighborhood of the laser target area. We are interested in the high-fidelity description of the multiphase fluid dynamics and solid mechanics in the neighborhood of the laser DE interactions, as well as the overall system response to the associated thermomechanical loading, which necessitates fully-coupled multi-physics formulations.

Commonly used uncoupled or loosely-coupled operator-splitting-based approaches do not provide satisfactory (i.e., effective, accurate, and robust) solutions. As an alternative, a formulation that is fully coupled and high order in both space and time should be used. In this project, we explored the current status of legacy multi-physics algorithms within Lawrence Livermore National Laboratory’s production-level ALE3D code and their suitability for laser DE potential lethality and vulnerability applications. We also investigated the applicability of recently developed high-order, implicit, spatiotemporal discretization using the discontinuous finite-element formulation (rDG) and L-stable method-of-lines methods, all within the tightly-coupled Newton–Krylov-based scalable, iterative method for generic conservation laws solved on unstructured meshes.

Impact on Mission

This project supports the NNSA goal to apply our science and technology to national security missions. The results of our research directly support the Laboratory’s mission focus and core competency of computational modeling. In addition to laser DE applications, a range of national security applications stand to greatly benefit from the explored fluid/structure modeling at extreme conditions, including the continuing efforts of ALE3D in advanced manufacturing and powder-bed fusion, the recently started efforts to develop high-fidelity implicit solvers for all-speed high-explosive cook-off events, and the potential for modeling aerodynamics and fluid-structure interactions in very high Mach-number flows for reentry body problems, which also require implicit discretization and related preconditioning of linear algebra to represent boundary-layer dynamics and thermostructural loadings.

Conclusion

As a result of the project, a number of important areas for future algorithmic- and physics-modeling developments were identified. The initial goal was to use the legacy implicit-hydro solver in ALE3D and couple it with ALE3D’s legacy thermal solver and the newly developed high-order, rDG-based fully-implicit fluid-dynamics solver. The coupling was designed to use the Jacobian-free Newton–Krylov (JFNK) methodology. We discovered that using legacy algorithms was not appropriate or effective, as some conceptual algorithmic and code-design flaws in the legacy solvers prevent effective implementation within the JFNK framework. Instead, the high-order, rDG-based solver was modified to enable modeling of both fluids and solids, and an initial demonstration of the fully-coupled simulations for laser-spot heating of solid shells, coupled with external fluid dynamics, was presented. The results have been published (Nourgaliev et al. 2018).

This approach was clearly effective and is recommended for future deployment in laser DE applications. These efforts should capitalize on the present findings.

  • The rather simplified material-strength method used in this limited-scope project should be extended and based on a detailed material-stress-dynamics model. This should be done within the fully implicit, high-order, spatiotemporal discretization in all-speed flow configurations to enable the large time-step simulations necessary for applications with laser DE heating.
  • Initial exploration of the approximate block factorization approach for preconditioning of the Krylov solver, developed and presented in (Weston and Nourgaliev, 2018), should be extended to the new high-fidelity material-strength model, using the nested approximate multi-block factorization for degrees of freedom evolved as independent variables in JFNK.
  • High-order degrees of freedom should be treated using the “p-multigrid” approach, which was shown to be effective for scalar (heatwave type) problems.
  • The effectiveness of the “p-multigrid” preconditioning for a system of equations (Navier–Stokes + energy and stresses) should be further extended and demonstrated in a wide range of flow conditions.

References

Nourgaliev, R., et al. 2018. "High-Order Fully-Implicit Solver for All-Speed Fluid Dynamics: AUSM Ride from Nearly-Incompressible Flows to Shock Dynamics," International Journal on Shock Waves, Detonations and Explosions. doi: 10.1007/s00193-018-0871-8. LLNL-JRNL-745590.

Weston, B., and R. Nourgaliev. 2018. "p-Multigrid" Block Reduction Preconditioning for a Fully-Implicit High-Order Reconstructed Discontinuous Galerkin Flow Solver. Poster at NECDC-2018, Los Alamos, NM, October 2018. LLNL-POST-759120.

Publications and Presentations

Greene, P., et al. 2017. "Marker Re-distancing (MRD) Algorithm for High-Fidelity Interface Tracking on Arbitrary Meshes." Proceedings of ASME 2017 Fluids Engineering Division Summer Meeting. Hawaii, August 2017. LLNL-PROC-722958.

Nourgaliev, R., et al. 2017. "Sharp Treatment of Multimaterial Interfaces in Fluid Dynamics." International Conference on Coupled Problems in Science and Engineering. Rhode Island, Greece, June 2017. LLNL-PRES-733025.

——— . 2018. "AUSM Ride from Nearly-Incompressible Flows to Shock Dynamics: High-Order Fully-Implicit All-Speed Solver." Proceedings of the 10th International Conference on Computational Fluid Dynamics (ICCFD10). Barcelona, Spain, July 2018. LLNL-CONF-753085.

——— . 2017. "Physics-Based Reconstruction of Interfacial Jump Conditions in All-Speed Multi-Fluid Dynamics." Proceedings of ASME 2017 Fluids Engineering Division Summer Meeting. Hawaii, August 2017. LLNL-CONF-722940.

——— . 2017. "High-Order Sharp Treatment of Interfacial Jump Conditions in Multi-Fluid Dynamics." MultiMat-2017, Santa Fe, September 2017. LLNL-PRES-738426.

——— . 2018. "Sharp-Interface Treatment of Multi-Material Discontinuities in Laser Directed Energy Applications." NECDC-2018, Los Alamos, NM, October 2018. LLNL-PRES-758893.

——— . 2018. "High-Order Fully-Implicit Solver for All-Speed Fluid Dynamics: AUSM Ride from Nearly-Incompressible Flows to Shock Dynamics." International Journal on Shock Waves, Detonations and Explosions. doi: 10.1007/s00193-018-0871-8. LLNL-JRNL-745590.

Rollins, C., et al. 2017. "Geometric Conservation Law for Mesh Motion and Fully Implicit rDG Methods." Poster presentation. LLNL. Livermore, August 2017. LLNL-POST-735502.

Weston, B. and R. Nourgaliev. 2018. "p-Multigrid" Block Reduction Preconditioning for a Fully-Implicit High-Order Reconstructed Discontinuous Galerkin Flow Solver. NECDC-2018, Los Alamos, NM, October 2018. LLNL-POST-759120.

Weston, B., et al. 2017. "Preconditioning of a High-Order, Fully-Implicit Compressible Flow Solver for Large-Scale Simulations of Multi-Physics Processes in Additive Manufacturing." International Conference on Coupled Problems in Science and Engineering. Rhode Island, Greece, June 2017. LLNL-PRES-732949.

——— . 2017. "Preconditioning for the All-Speed Compressible Navier–Stokes Equations with Laser-Induced Phase Change." Proceedings of ASME 2017 Fluids Engineering Division Summer Meeting, Hawaii, August 2017. LLNL-PROC-723820.