Project Title: "Python Simulation of Shock-Turbulence Interactions in Complex Fluid Flows"

Objective: Develop a Python-based simulation framework to study shock-turbulence interactions in complex fluid flows and investigate their effects on turbulent mixing and plasma physics phenomena.

Steps:

Numerical Simulation Framework: Develop a Python-based numerical simulation framework that integrates large-eddy simulations (LES) and shock-capturing methods to model turbulent flows and shock interactions in different physical scenarios.

Turbulence Modeling: Implement turbulence models, such as Smagorinsky-Lilly or dynamic Smagorinsky, within the LES framework to accurately simulate turbulent flows and resolve turbulent structures.

Richtmyer-Meshkov Instability: Incorporate numerical methods to model the Richtmyer-Meshkov instability at solid-gas interfaces and elastic-plastic solids. Implement the equations from relevant papers to simulate these interactions.

Plasma Physics Module: Integrate a plasma physics module into the simulation framework to study hollow cathode physics and its implications on plasma potential and work function distribution.

Validation and Verification: Validate the simulation framework by comparing the simulation results with experimental data from shock-turbulence interaction experiments and plasma potential measurements.

Visualization and Analysis: Develop data visualization tools using Python libraries such as Matplotlib and PyVista to visualize the simulation results in 2D and 3D. Use Python's scientific computing libraries to analyze turbulence statistics, shock structures, and plasma properties.

Parameter Sensitivity Study: Conduct a sensitivity study to investigate the influence of various parameters, such as Reynolds number, Mach number, and material properties, on shock-turbulence interactions and plasma behavior.

Parallelization: Optimize the simulation framework for parallel computing using Python libraries like MPI4py to expedite the computational process and enable large-scale simulations.

Code Documentation and Sharing: Document the Python simulation framework and make it open-source to allow collaboration and contributions from the scientific community.

Research Paper and Dissemination: Summarize the findings, methodology, and implications in a research paper. Present the results at relevant conferences and share the simulation framework with the research community.