What are the key design parameters and recommended methods for accurate sizing and calculations of a variable nozzle for a jet engine?

I am working on the design of a variable nozzle for a jet engine and seeking guidance on the critical factors influencing its performance and sizing. Specifically, I am interested in:

1. Key design parameters such as throat area, expansion ratio, nozzle geometry, and materials for thermal resistance.

2. Methods for determining the optimal nozzle area variation for different engine operating conditions.

3. Strategies for integrating variable nozzles with afterburners and their impact on thrust and efficiency.

4. Recommendations for simulation tools or empirical methods to analyse flow characteristics, thermal stresses, and mechanical durability.

If you have experience in designing or simulating variable nozzles, I would appreciate any insights, tools, or references that could support accurate calculations and enhance my design process.