Models and Numerical Algorithms for Hydrodynamics with Atomic Processes and High Energy Density Applications.

摘要

The main goal of the research is the development of numerical equation of state model enabling hydrodynamic simulations of problems involving multiple ionization and it's application in the high energy density physics (HEDP) such as the plasma jet driven magnetoinertial fusion (PJMIF) concept and the pellet injection in Tokamak via simulations studies. For this goal, the mathematical models and numerical algorithms for ionization process has been developed, and they are demonstrated in several simulations with productive result.;A numerical model for an average ionization equation-of-state (EOS) for high-Z plasmas undergoing multiple ionization processes has been developed by improving the classical Zeldovich model. The corresponding software library has been implemented in FronTier, a hydrodynamic code that explicitly tracks material interfaces via the front tracking method. Implementation required an efficient coupling of the EOS model with Riemann solver algorithms used in high resolution hyperbolic solvers. By partially replacing costly nonlinear solvers with precomputed data sets, we were able to speedup computations by two orders of magnitude. The EOS model was verified with respect to a standard benchmark problem involving solutions of coupled systems of Saha equations.;The FronTier code with this EOS model has been used for simulations of formation and implosion of plasma liners in the concept of PJMIF. The PJMIF is an alternative method proposed to combine features of the inertial and magnetic confinement nuclear fusion to solve the standoff problem. We performed modeling and simulations of processes relevant to PJMIF and investigated the effect of atomic processes and the internal structure of plasma liner during self-implosion. In idealized simulations of plasma liners and targets in spherical symmetry, we analyzed the liner efficiency, target compression rates, fusion energy gains, and quantified the effect of atomic processes on the liner and target compression. In 2-dimensional (2D) and 3-dimensional (3D) simulations of plasma jets merger, a cascade of oblique shock waves was observed in the merger process of discrete plasma jets. This observation explained the structure of plasma liners and agreed well with theoretical analysis.;Spherically-symmetric simulations of the pellet ablation in tokamaks, a nuclear fusion device based on magnetic confinement, have also been performed using the FronTier code equipped with the EOS for atomic processes. The pellet injection into tokamaks is proposed as a very efficient method for the fusion fuel supply and the plasma disruption mitigation. We performed studies of the ablation rate and the properties of ablation flow using our numerical tool. For more accuracy in the low temperature region, we upgraded the average ionization model by including the continuum assumption of statistical weights of ionization level. The ablation rate of neon and argon pellets decreased due to ionization-induced energy sinks, and the ablation flow reached a multi-transonic state similar to that observed in deuterium pellets.