Numerical Simulation Of Fluid Instability In Icf Research And Hamilton-jacobi Equations Of Motion Grid Method

Hamilton-Jacobi equations have been widely applied to various fields, such as, optimal control theory, computational fluid dynamics, computing vision, differential geometry, crystal growth, mesh generation. In the past years, the research on the Hamilton-Jacobi equations has attracted much attention. It is well-known that the solutions of the Hamilton-Jacobi equations are continuous but with discontinuous derivatives, even the initial values and the Hamiltonian are smooth. And such solutions are in general not unique. The first part of this thesis is concerned with the numerical solution of the Hamilton-Jacobi equations. A numerical scheme is presented for solving the Hamilton- Jacobi equations by applying adaptive moving mesh methods based on level-set-based deformation. Numerical examples are given, which demonstrate the accuracy and efficiency of computing "extremes" and "spikes" of solution to the Hamilton-Jacobi equations. Hydrodynamic instability is one of the most important issues arising from Inertial Confinement Fusion (ICF) ignition, and influences implosion and inertial confinement fusion ignition. To enhance implosion efficiency and decrease energy of laser facility, ICF in general utilizes large convergent ratio, high aspect fusion targets. The growth of perturbation in fusion targets is driven by acceleration/deceleration (Rayleigh-Taylor), influencing implosion and the ICF ignition. With the development of perturbation, thermal spikes feedthrough thin shell, penetrating and then heating up DT material, damaging high compressibility of the DT material, therefore affecting the ignition. Numerical simulations of the laser ablative interface instability of the inertial confinement fusion are the second part of this thesis.The thesis consists of three chapters. In Chapter 1, we briefly review the developments on theoretical analysis and numerical methods for the Hamilton-Jacobi equations and on numerical simulation of Inertial Confinement Fusion laser ablative interface instability, then the main results of this thesis are presented. In Chapter 2, a numerical scheme is presented for solving Hamilton-Jacobi equations by applying adaptive moving mesh methods based on level-set-based deformation. The advantages of the adaptive moving mesh methods based on level-set-based deformation are that the local adjusted meshes trace discontinuities automatically and can improve the accuracy and resolution. Numerical examples illustrate these advantages. In Chapter 3, we study numerical simulations of the two-dimensional hydrodynamic instability and the laser ablative interface instability of the ICF by applying the level-set method and ENO (Essentially Non- Oscillatory) on a adaptive moving mesh, comparing with the Lared-s code , the numerical results show the improvement in interface accuracy and resolution of capturing interfaces.