Research Overview  

A central objective of my research is to investigates the physics of the Richtmyer-Meshkov instability.

The Richtmyer-Meshkov instability is a fundamental fluid instability that occurs when perturbations on an interface separating gases with different properties grow following the passage of a shock. This instability is of great fundamental interest in fluid dynamics, as well as of interest to inertial confinement fusion, and to supernovae dynamics.

The instability derives its name from the linear instability analysis and numerical simulations of Richtmyer [Comm. Pure Appl Math. 8, 297 (1960)], and the shock tube experiments of Meshkov [Sov. Fluid Dyn. 4, 101 (1969)]

The goal of this research is two-fold;

1. understand the evolution of the instability, model the growth of the mixing layer in the nonlinear phase and following reshock, as well as predict the statistical properties and dynamics of turbulent mixing induced by the instability.
2. understand the large scale dynamics of the instability, including the bubble and spike dynamics, interface stretching, and large scale properties of the instability.
   

Two numerical methods are employed in the investigation as they offer complementary views of flow features

1. the compressible Euler equation solver based on the Weighted Essentially Non-Oscillatory (WENO) shock capturing method, is used to determine the dynamics of the mixing layer, as well as the statistical and turbulent properties of mixing
   
2. the incompressible vortex method is used to model the bubble and spike dynamics, and the interface evolution

• Thesis Title: Investigation of the Richtmyer-Meshkov Instability in Complex Geometries Using the Weighted Essentially Non-Oscillatory method and Vortex Methods
  

Research Goals
 
A central objective of the present work is to establish a systematic procedure to investigate the dynamics of the mixing process induced by the Richtmyer-Meshkov instability, and more generally by complex hydrodynamic flows. The methods used are adapted from classical investigations of turbulence and turbulent mixing, and synthesize high-resolution numerical simulation data, theoretical models for instability growth, and available experimental data. This procedure results in:

1. the application of a modern, high-resolution, flexible numerical method that has been validated against available experimental data;
   
2. a numerical database that provides quantities that can be compared to model predictions and to experimental measurements, as well as quantities that have not been modeled (or are difficult to model) or are not available experimentally;
   
3. numerical data for configurations extended to times beyond what is possible to achieve experimentally, or for configurations that are difficult to achieve experimentally;
   
4. a systematic understanding of the important effects of spatial resolution and formal order of the method on quantities of interest to modeling the instability evolution and mixing.