Analytical and Computational Techniques for Fluid Flows Interacting With Intense Radiation Fields

Abstract

The field of high-energy-density (HED) physics features many problems of impor- tance to society, including stellar formation in astrophysics as well as next-generation energy technologies. Often, these systems involve complex fluid flows, such as mixing between different fluids, that are influenced by radiation fields. Predicting the evolution of these systems requires understanding the role of the two-way coupling between radiation and the fluid flow. The development of experimental techniques for creating and diagnosing HED systems has greatly expanded our understanding of their evolution. However, these experiments are challenging, and the state of HED plasmas often cannot be completely constrained by available diagnostics. Analytical and computational tools provide valuable insight in predicting quantities that may be difficult to glean from experiments. Intense sources of radiation drive ablative flow in many applications, generating impulse and driving a compression wave into the bulk material. Analytical models exist to predict the impulse generated in materials exposed to radiation, but they de- pend on the energy of the blown-off material, which in general is not known due to the complex partitioning of energy that occurs in the system. The uncertainty associated with measurements of x-ray spectra poses another difficulty in predicting the impulse generated in an irradiated material. We address these issues via a data-driven approach to modeling the impulse generated in materials exposed to a given x-ray source spectrum. We use data from high-fidelity simulations to inform an analytical model for the impulse generated in a given material by an arbitrary radiation source. This model also provides an analytical form for the impulse-spectrum sensitivity, a quantity that is important for constraining the uncertainty in impulse resulting from uncertainty in the source spectrum. The model for the impulse-spectrum sensitivity agrees well with the sensitivity evaluated directly from simulations, requires significantly less computation time, and can also be evaluated using data from experiments. This work enables low-cost prediction of important quantities in the radiation-generated impulse in materials. The modeling approach we propose greatly simplifies the study of such systems, as well as the design of robust experiments. Numerical simulation of HED systems poses a challenge, as the problems tend to be multi-scale and involve fundamentally different, often competing, physical processes. The discontinuous Galerkin (DG) method offers many advantages, particularly as computing architectures evolve to offer exascale capabilities. In particular, DG offers arbitrarily high-order accuracy with a compact stencil, making it well-suited for parallel scaling. However, high-order methods have seen limited application to the study of HED systems. As we are primarily interested in the study of multimaterial flows in intense radiation fields, we extend interface capturing techniques used for classical fluid flows to radiation hydrodynamics in the framework of the DG discretization. Our approach uses a careful, physically consistent treatment of material interfaces, including a limiting procedure designed to prevent unphysical errors that occur from other approaches. This development results in an approach that is high-order accurate, conservative, physically consistent, and well-suited for parallel computation of radiation hydrodynamics. We demonstrate these properties of the method using one- dimensional verification problems, as well as a two-dimensional problem relevant to HED science. This work demonstrates the promising application of high-order numerical methods to practical problems in HED science, a field that has seen limited application of such methods.