Project Grant 2208438

The National Science Foundation awarded North Carolina State University a three-year, $368,594 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049) to develop new mathematical and computational tools for nonlinear hyperbolic systems of partial differential equations. The university will use the funding to design efficient high-order numerical methods for conservation and balance laws that go beyond consistency, stability, and convergence. Key activities include developing techniques to balance numerical diffusion and dispersion for sharp yet non-oscillatory resolution of shock and contact waves while achieving high accuracy in smooth regions, and establishing asymptotic preserving properties in stiff regimes. The grant also supports training graduate students. The tools and techniques developed through this research have the potential for broad application in fluid dynamics, astrophysics, meteorology, oceanography, and other scientific domains involving hyperbolic systems, and will advance understanding of important physical phenomena.