Fan Zheng-Feng

Weak Nonlinearity of Ablative Rayleigh–Taylor Instability

The weakly nonlinear regime of single mode ablative Rayleigh–Taylor instability is studied, with consideration of preheat effect and the width of the ablation front. The Rayleigh–Taylor linear growth rate agrees well with the direct numerical simulation. For the density perturbation, the amplitude distribution of the fundamental mode has one peak value whereas those of the second and third harmonics have two and three peak values, respectively. Harmonics generation versus wave number is also given and it is close to the result of direct numerical simulation.

Compressible Rayleigh–Taylor Instability with Preheat in Inertial Confinement Fusion

The compressible Rayleigh–Taylor instability of accelerated ablation front is analysed in consideration of the preheat effects, and the corresponding eigen-problem is solved numerically using the fourth-order accurate two-point compact difference scheme. Both the growth rate and perturbation profiles are obtained, and the obtained growth rate is close to the results of direct numerical simulation. Our results show that the growth rate is more reduced and the cutoff wave length becomes longer as preheat increases.

Nonlinear Evolution of Jet-Like Spikes from the Single-Mode Ablative Rayleigh-Taylor Instability with Preheating

In this research, the nonlinear evolution of jet-like spikes in the single-mode ablative Rayleigh-Taylor instability (ARTI) in the presence of preheating, is studied numerically. It is demonstrated that the preheating plays an essential role in the formation of jet-like spikes in the nonlinear ARTI. The evolution of jet-like spikes in the ARTI with preheating consists of three stages with distinctly different distinguishing features. In the early stage, the preheating contributes to significantly increase the density-gradient scale length and broaden the velocity profile of the ablation surface, where the former can reduce the linear growth of the ARTI and mitigate the growth of its harmonics. In the middle stage, the ablative Kelvin-Helmholtz instability is dramatically suppressed due to the ablation effects. In the late stage, the jets length (i.e. bubble-spike amplitude) is further increased by the bubble acceleration in the highly nonlinear ARTI, resulting eventually in the formation of jet-like spikes.

A Weakly Nonlinear Model for Kelvin–Helmholtz Instability in Incompressible Fluids

A weakly nonlinear model is proposed for the Kelvin–Helmholtz instability in two-dimensional incompressible fluids by expanding the perturbation velocity potential to third order. The third-order harmonic generation effects of single-mode perturbation are analyzed, as well as the nonlinear correction to the exponential growth of the fundamental modulation. The weakly nonlinear results are supported by numerical simulations. Density and resonance effects exist in the development of mode coupling.

Multimode Coupling Theory for Kelvin?Helmholtz Instability in Incompressible Fluid

A weakly nonlinear model is proposed for multimode Kelvin–Helmholtz instability. The second-order mode coupling formula for Kelvin–Helmholtz instability in two-dimensional incompressible fluid is presented by expanding the perturbation velocity potential to second order. It is found that there is an important resonance in the course of the sum frequency mode coupling but the difference frequency mode coupling does not have. This resonance makes the sum frequency mode coupling process relatively complex. The sum frequency mode coupling is strongly dependent on time especially when the density of the two fluids is adjacent and the difference frequency mode coupling is not.

Studying Validity of Single-Fluid Model in Inertial Confinement Fusion

The validity of single-fluid model in inertial confinement fusion simulations is studied by comparing the results of the multi- and single-fluid models. The multi-fluid model includes the effects of collision and interpenetration between fluid species. By simulating the collision of fluid species, steady-state shock propagation into the thin DT gas and expansion of hohlraum Au wall heated by lasers, the results show that the validity of single-fluid model is strongly dependent on the ratio of the characteristic length of the simulated system to the particle mean free path. When the characteristic length L is one order larger than the mean free path λ, the single-fluid models results are found to be in good agreement with the multi-fluid models simulations, and the modeling of single-fluid remains valid. If the value of L/λ is lower than 10, the interpenetration between fluid species is significant, and the single-fluid simulations show some unphysical results; while the multi-fluid model can describe well the interpenetration and mix phenomena, and give more reasonable results.

Phase Effect on Mode Coupling in Kelvin—Helmholtz Instability for Two-Dimensional Incompressible Fluid

This paper studies the phase effect in mode coupling of Kelvin–Helmholtz instability in two-dimensional incompressible fluid. It is found that there is an important growth phenomenon of every mode in the mode coupling process. The growth changes periodically with phase difference and in the condition of our simulation the period is about 0.7π. The period characteristic is apparent in all stage of the mode coupling process, especially in the relatively later stage.

Simulation of Kelvin–Helmholtz Instability with Flux-Corrected Transport Method

The sixth-order accurate phase error flux-corrected transport numerical algorithm is introduced, and used to simulate Kelvin–Helmholtz instability. Linear growth rates of the simulation agree with the linear theories of Kelvin–Helmholtz instability. It indicates the validity and accuracy of this simulation method. The method also has good capturing ability of the instability interface deformation.