- Numerical Analysis
- Numerical Modeling
- Numerical Simulation
- Computational Fluid Dynamics
- CFD Simulation
- Finite-Difference Schemes
- Semi-Implicit and IMEX Schemes
- Finite-Volume Schemes
The primary objective of my research is to develop efficient numerical techniques for simulating a wide range of physical phenomena. These methods should balance computational cost and accuracy, minimizing waste and errors.
My research focuses on modeling and simulating hyperbolic systems with conservation and balance laws. These systems involve complex wave interactions and discontinuities. By studying them, I aim to develop numerical schemes that accurately capture their dynamics while being computationally efficient.
I investigate well-known benchmark problems like the Sod shock problem and piston problem. These problems test the performance of numerical methods in accurately capturing shock waves and discontinuities. By developing efficient schemes for these problems, I establish the reliability of the techniques.
I also model environmental and geophysical phenomena, such as the shallow water behavior. Accurately simulating these systems contributes to understanding events like coastal evolution, sedimentation, and wave behavior in estuaries.
My research extends to multiscale simulation techniques, which model phenomena at different scales. This is relevant in complex systems with interactions between scales. By efficiently capturing the multiscale nature, I aim to improve understanding and prediction accuracy.
I investigate the design and implementation of efficient numerical schemes to minimize computational costs while maintaining accuracy. This improves accessibility and cost-effectiveness of simulations.
In summary, my research develops numerical techniques that balance computational cost and accuracy. Focusing on hyperbolic systems and their applications, I advance numerical simulation while minimizing waste and errors.