This project will attempt to combine algorithm development for high order accurate, weighted essentially non-oscillatory schemes for solving high speed, high Mach number inviscid flows containing strong shocks and other complex flow structures, with cosmological applications in hydrodynamic simulations. The objective is to develop efficient and robust numerical methods for cosmological applications, and to consider the hydrodynamics of the epoch of reionization, the hydrodynamical behavior of baryon gas around dark matter singularities, the statistical discrepancy between the intergalactic medium and dark matter in the non-linear regime of clustering, the entropy production of gravitational shocks, and other complex structural problems. Addressing cosmology's unique difficulties, such as the existence of extremely strong singularities and the effective coupling of hyperbolic hydrodynamic equations with elliptic equations for self-gravity, requires advances in computational mathematics and scientific computing.
Broader impacts include enhancing a collaboration across two universities, advancing the mathematical sophistication of astrophysics, and making algorithms and codes of general utility available to the wider astrophysics, physics, and engineering communities.
