Numerical simulation is presented as a core tool in modern physics and engineering, used to study systems that are too complex for analytical solutions or direct experiments. The research focuses on developing and applying computational models that solve the fundamental equations governing fluids, plasmas, and other physical systems.

A central theme is the simulation of fluid dynamics across a wide range of regimes, from subsonic to hypersonic flows. The work emphasizes accurate resolution of shocks, turbulence, boundary layers, and instabilities. To achieve this, high order numerical schemes, adaptive mesh refinement, and robust time integration methods are developed and tested. These techniques aim to balance accuracy, stability, and computational cost on modern high performance computing architectures.

Another key area is plasma physics, where simulations are used to study magnetized plasmas, kinetic effects, and wave particle interactions. Both fluid models, such as magnetohydrodynamics, and kinetic models, such as particle in cell approaches, are explored. The research investigates how microscopic processes shape macroscopic behavior in laboratory and astrophysical plasmas.

There is also a focus on multiphysics coupling, where different physical processes and scales interact. Examples include radiation hydrodynamics, reactive flows, and flows in complex geometries. The work examines numerical strategies to couple equations consistently and to control numerical errors that can propagate across coupled components.

Overall, the research highlights numerical simulation as a virtual laboratory, enabling controlled experiments on models that incorporate detailed physics, and providing insights that guide theory, design, and interpretation of observations.