Part I. Astrophysical applications of fluid dynamics. - Euler’s equations of fluid dynamics, - selfgravitating fluids - Poisson’s equation - sound waves, shock waves, supernova explosions, - fluid instabilities: convective, Raileigh-Taylor, Kelvin-Helmholtz, gravitational and thermal instabilities, - Bernouli’s equation, spherical accretion and winds, - viscous flows, Navier-Stokes equation, Reynolds number, - vorticity equation, Kelvin’s theorem of vorticity conservation, - turbulence and its astrophysical significance, - hydrodynamics of accretion disks, - hydrodynamical processes in star formation activity. Part II. Numerical methods for fluid dynamics. - elements of the theory of partial differential equations, method of characteristics, Riemann problem, Rankine-Hugoniot relations, linear hyperbolic systems - conservative form of hydrodynamics equations, shock waves, rarefaction waves and the solution of Riemann problem in fluid dynamics. - basic numerical methods for partial differential equations, von Neuman stability analysis of numerical schemes, - Riemann solvers and Godunov methods for fluid dynamics.
