Level Set Methods for Multimaterial Radiative Shock Hydrodynamics

[摘要] Multimaterial radiative-hydrodynamic flows containing shockwaves are ubiquitous in high energy density physics (HEDP). Numerical models are critical for the prediction and study of phenomena such as radiation-driven outflows and inertial-confinement fusion. Flow dynamics are especially sensitive to the treatment of material interfaces and the discretization of material-dependent quantities. Errors in numerical models arise due to inconsistent measures of width for material interfaces: physical width determined through material dissipation and mixing, modeling width determined by a mathematical model for interface representation, and numerical width determined by numerical diffusion.HEDP flows in this thesis occur over short timescales, with physical interfaces well approximated by sharp discontinuities. The level set (LS) model represents interfaces in a manner consistent with physical assumptions, with modeling width on the order of the mesh spacing. Numerical width is much larger due to the use of shock-capturing hydro solvers. Numerical errors result from interactions between numerically-diffused flow variables and material discontinuities.Numerical diffusion acting across sharp interfaces can generate significant losses in species mass conservation, influencing the transport of energy throughout the system. Errors in pressure and temperature computed from diffused flow variables can trigger spurious interfacial instabilities. Numerical diffusion acting on LS functions can lead to ambiguities in the representation of interfaces and triple junctions when three or more materials are present.A new LS framework is developed for two-dimensional flows which addresses these errors. The new LS functions are robust to numerical diffusion effects and are capable of modeling an arbitrary number of materials in a manner free of interface ambiguities. Interface geometry is well defined, and methods are presented for computing both continuous sub-cell interface reconstructions and consistent volume fractions from discrete LS data. Errors in pressure, temperature, and species mass are analyzed and connections are drawn to radiative-hydrodynamic flows. Additional modifications to the LS model are introduced to reduce or remove these errors, with numerical results comparing favorably to existing methods.

[发布机构] University of Michigan

[效力级别] Multimaterial

[关键词] Radiation-hydrodynamics;Multimaterial;Level Set;Compressible Fluid Flow;Interfaces;Non-conservative Hyperbolic System;Mathematics;Science;Applied and Interdisciplinary Mathematics