Astrohydrodynamics (Astrophysical Fluid Dynamics)

1. knowledge of linear algebra and calculus.

2. basic knowledge of mechanics and thermodynamics.

Contact hours with teacher:

- participation in lectures - 30 hrs

- participation in tutorials - 15 hrs

Self-study hours:

- preparation for lectures - 30 hrs

- preparation for tutorials – 15 hrs

- preparation for examination- 30 hrs

Altogether: 120 hrs (4 ECTS)

Student

W1: knows bases of fluid dynamics and understands its role inastrophysics. (K_W04, K_W06)

W2: is able to use analytical calculation methods for theoretical investigations of fluid dynamical phenomena in astrophysics. (K_W01)

W3: knows theoretical bases of numerical algorithms for fluid dynamics equations. (K_W02, K_W03)

Student

U1: is able to use analytical calculation methods for theoretical investigations of fluid-dynamical phenomena in astrophysics.

(K_U03)

U2: Can use and modify available software for numerical modeling fluid-dynamical phenomena in astrophysics. (K_U04)

Student

K1: understands the importance and limitation of mathematical and numerical modeling in fluid dynamis. (K_K01)

Lectures: Expository teaching methods - informative lecture.

Tutorials: Exploratory teaching methods - computer laboratory for training numerical methods in fluid dynamics.

- simulation (simulation games)

- participatory lecture

- laboratory

- games and simulations

The aim of the lecture is to present bases of fluid dynamics and

its application in description of astrophysical phenomena.

The lecture will include the following topics:

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.

1. The Physics of Fluids and Plasmas, Arnab Rai Choudhuri, Cambridge University Press, 1998

2. "Principles of Astrophysical Fluid Dynamics", C.J. Clarke, R.F. Carswell, Cambridge University Press, 2014

3. "Gas dynamics" F.H. Shu, University Science Books 1992

4. „Riemann solvers and Godunov methods in fluid dynamics”, E.F Toro, Springer 1997.

Assessment methods:

- lecture: written examination (W1, W2, W3, U1, K1).

- tutorials: activity at the computer laboratory tutorials (U2) and evaluation of written reports on the programming work and numerical experiments performed at the computer laboratory.

Assessment criteria:

fail: < 50%

satisfactory: 50-59%

satisfactory plus: 60-69%

good: 70-79%

good plus: 80-89%

very good: 90-100%

„not applicable”