Scalable Computational Tools for Predicting Fluid-Structure Interactions in Laser Directed Energy Applications

Project Overview

This project is motivated by the need for accurate, robust and computationally-efficient tools to model long time-scale processes (seconds to minutes) of laser-driven directed energy (DE) material heating, melting, and interaction with external fluid flows. While there are many hydrodynamic codes capable of describing short time-scales (milliseconds), they are all based on explicit time discretizations, limited by time steps resolving the fastest/stiffest time scales (typically, unimportant, associated with propagation of sound waves in a material), and are inefficient for longer transients. Fully-implicit methods, on the other hand, can step over unimportant time scales, accurately resolving only those of interest, dynamic time-scales (associated with thermal wave propagation, material motion, or slow/nearly-stationary shock speeds). Moreover, we are interested in methods capable of describing the physics for both fluid and solid dynamics, as well as the complex physics of interactions at multi-material fluid-fluid and fluid-solid interfaces, including phase transition (melting), localized thermal energy deposition with potentially recoil pressure effects, material entrainment by external turbulent flows, complex surface chemistry, etc.

In this project, we have developed an innovative high-order space-time moving-mesh discontinuous Galerkin (MDG) method with interface condition enforcement (ICE). This MDG-ICE method is designed to simultaneously solve conservation laws and to move the mesh (generally, curvilinear in both space and time), aligning the faces of finite elements with all physical solution discontinuities (shocks, contacts, front/tails of rarefaction waves, etc.). Since time is numerically treated the same way as space, the method is intrinsically implicit. This method belongs to the class of implicit shock-(discontinuity)-fitting, as opposed to traditionally used shock-capturing. Importantly, the MDG-ICE is capable of delivering high-order convergence even in the presence of discontinuities. This is unique, as no existing shock-capturing method is truly high-order accurate. MDG-ICE is capable of unveiling the full power of a discontinuous finite-element methodology, with the physics of discontinuities/interfaces is described by implicitly-solved interface jump conditions, casted in a weak form of a finite-element representation of conservation on element faces (interfaces), while the physics of governing PDE equations is described by traditional discontinuous Galerkin formulations inside of each space-time element. Since no artificial viscosity is needed/added, we have demonstrated that the method is converging with consistent high-order accuracy upon mesh (h-) refinement, and exponentially converging with polynomial (p-) refinement, in contrast to traditional shock capturing methods, which are first-order accurate at best in the presence of discontinuities (due to added artificial viscosity), even when a nominally high-order discretization is utilized. Furthermore, we have demonstrated how the MDG-ICE method can be extended for modeling material strength. We have experimented with both hypoelastic and hyperelastic formulations, using either Jaumann-rate formulation or recently developed Godunov-Peshkov-Romenski (GPR) models. Both are found compatible with MDG-ICE, and capable of very accurate representation of Cauchy stresses in elastic and elasto-plastic materials subjected to shocks. In addition, this new MDG-ICE method is found to be very accurate for modeling of solid-solid contact problems. The method is working very well for equations with parabolic operators, capable of accurately resolving very thin thermal and viscous boundary layers formed under very high-speed (transonic, supersonic) flow conditions. Finally, substantial progress has been achieved in developing robust non-linear solver methodology for simulation of vortical fluid flows and interaction of shocks with multi-material fluid-fluid and fluid-solid interfaces.

Mission Impact

The proposed effort directly supports the national security mission focus area and the core competency of computational modeling. This project develops science and technology tools and capabilities to meet future national security challenges, ultimately enabling NNSA to create new ways of responding to national security challenges.

Publications, Presentations, and Patents

Luo, H., Absillis, G., and Nourgaliev, R. 2022. "A Moving Discontinuous Galerkin Method with Interface Conservation Enforcement for Compressible Multi-material Flow Problems." In AIAA Scitech 2022 forum, San Diego, California, January 3-7, 2022.

Nourgaliev, R., Corrigan, A., Kercher, A., Wopschall, S., and Greene, P. 2021. "Implicit shock fitting for multimaterial shock dynamics using a high-order space-time discontinuous finite-element method." In ANS M&C 2021 - The International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, USA, Raleigh, North Carolina. October 3-7, 2021.

Kercher, A., and Corrigan, A. 2021. "A least-squares formulation of the moving discontinuous Galerkin finite element method with interface condition enforcement," Computers & Mathematics with Applications 95 (2021) 143-171. doi:10.1016/j.camwa.2020.09.012.

Kercher, A., Corrigan, A., and Kessler, D. 2021. "The moving discontinuous Galerkin finite element method with interface condition enforcement for compressible viscous flows," International Journal for Numerical Methods in Fluids 93 (5) (2021) 1490-1519. doi:10.1002/fld.4939.

Luo, H., Absillis, G., and Nourgaliev, R. 2021. "A moving discontinuous Galerkin finite element method with interface condition enforcement for compressible flows," Journal of Computational Physics, 445: 110618.

Kercher, A., Corrigan, A., Guthrey, P., and Nourgaliev, R. 2021. "Application of MDG-ICE to Shock Material Interface Interactions." AIAA AVIATION 2021 Forum, https://doi.org/10.2514/6.2020-0562.

Kercher, A., Corrigan, A., and Kessler, D. 2020. "The Moving Discontinuous Galerkin Method with Interface Condition Enforcement for Viscous Flows." AIAA Science and Technology Forum and Exposition 2020. https://doi.org/10.2514/6.2020-1315.

Corrigan, A Kercher, A., Kessler, D., and Wood-Thomas, D. 2019. "Convergence of the moving discontinuous Galerkin method with interface condition enforcement in the presence of an attached curved shock." In: AIAA (Ed.), 2019 AIAA AVIATION Forum, 2019, AIAA-2019-3207. doi:10.2514/6.2019-3207.

Nourgaliev, R., Wopschall, S., and Greene, P. 2021. "High-order Shock Fitting for Multimaterial Shock Dynamics Problems using Space-Time Finite-Element Formulation." Presentation at the SIAM Conference on Computational Science & Engineering (CSE21), virtual, Fort Worth, Texas. March 1-5, 2021.

Corrigan, A., and Kercher, A. 2021. "Complex Multi-Material Shock Interactions Using the Moving Discontinuous Galerkin Method with Interface Condition Enforcement." Presentation at the SIAM Conference on Computational Science & Engineering (CSE21), virtual, Fort Worth, Texas. March 1-5, 2021.

Guthrey, P., Nourgaliev, R., and Wopschall, S. 2021. "Moving Discontinuous Galerkin Finite Element Methods with Interface Condition Enforcement for the Godunov Peshkov Romenski Model of Material Strength." Presentation at the SIAM Conference on Computational Science & Engineering (CSE21), virtual, Fort Worth, Texas. March 1-5, 2021.

Nourgaliev, R., Corrigan, A., Kercher, A., Wopschall, S., Greene, P., and Guthrey, P. 2021. "High-order Implicit Shock Fitting for Multimaterial Shock Dynamics Problems using Space-Time Discontinuous Galerkin Formulation." Presentation at the Nuclear Explosive Code Development Conference (NECDC-2021), virtual, Livermore, California. May 10-14, 2021.

Guthrey, P., Corrigan, A., Wopschall, S., and Nourgaliev, R. 2021. "The Moving Discontinuous Galerkin Method with Interface Condition Enforcement for Shock Dynamics with Material Strength." Presentation at the Nuclear Explosive Code Development Conference (NECDC-2021), virtual, Livermore, California. May 10-14, 2021.

Kercher, A., Corrigan, A., and Kessler, D. 2021. "Applications of a Moving Discontinuous Galerkin Method with Interface Condition Enforcement." ICOSAHOM 2021, July 12-16, 2021, Vienna, Austria.

Guthrey, P. 2021. "High-order Implicit Shock Fitting for Multimaterial Shock Dynamics Problems using Space-Time Finite-Element Formulation." Presentation at the Weapons Complex Integration (WCI) DPD WIP Seminar, virtual, Livermore, California. July 8, 2020.

Corrigan, A., Kercher, A., and Nourgaliev, R. 2020. "The Moving Discontinuous Galerkin Method with Interface Condition Enforcement." MoST 2020: Modeling and Simulation of Transport Phenomena Workshop 2020, Virtual Conference, October 14, 2020.

Luo, H., Jiang, Y., and Nourgaliev, R. 2020. "A Moving Discontinuous Galerkin Method for Conservation Laws." AIAA Scitech 2020 forum, 6-10 January, 2020, Orlando, FL, AIAA-2020-1316, 2020.

Nourgaliev, R., and Corrigan, A. 2020. "High-order Implicit Shock Fitting for Multimaterial Shock Dynamics Problems using Space-Time Finite-Element Formulation." Presentation at the Weapons Complex Integration (WCI) DPD WIP Seminar, virtual, Livermore, California. July 8, 2020.

Corrigan, A., Kercher, A., Kessler, D., Wopschall, S., and Nourgaliev, R. 2019. "A moving discontinuous Galerkin method with interface condition enforcement applied to multi-material flows." In: Proceedings of the 9th international conference on Numerical methods for multi-material fluid flow (MultiMat2019), Trento, Italy. September 9-13, 2019.

Kercher, A., Corrigan, A., Kessler, D., and Mott, D. 2019. "A moving discontinuous Galerkin method with interface condition enforcement for incompressible flows with surface tension." In: Proceedings of the 9th international conference on Numerical methods for multi-material fluid flow (MultiMat2019), Trento, Italy. September 9-13, 2019.

Luo, H., Jiang, Y., and Nourgaliev, R. 2019. "A Moving Discontinuous Galerkin Finite Element Method for Conservation Laws." In: Proceedings of the 9th international conference on Numerical methods for multi-material fluid flow (MultiMat2019), Trento, Italy. September 9-13, 2019.

Nourgaliev, R., 2019. "Sharp-Interface (SI) Treatment of Multi-Material Discontinuities in Laser Directed Energy Applications." Presentation at the UC Davis Department of Mechanical & Aerospace Engineering Graduate Seminar, Davis, California. January 10, 2019.