Nonlinear spherical gravitational downfall of gas onto a solid ball: analytic and numerical results

Details Nonlinear spherical gravitational downfall of gas onto a solid ball: analytic and numerical results Nonlinear spherical gravitational downfall of gas onto a solid ball: analytic and numerical results

2003-09-23

arxiv.org/abs/nlin/0309064v2

PhysicaD183:102-116,2003

Nonlinear Sciences

Exactly Solvable and Integrable Systems

19 pages, 10 PS figures (some large)

Scientific paper

10.1016/S0167-2789(03)00157-X

The process of downfall of initially homogeneous gas onto a solid ball due to the ball's gravity (relevant in astrophysical situations) is studied with a combination of analytic and numerical methods. The initial explicit solution soon becomes discontinuous and gives rise to a shock wave. Afterwards, there is a crossover between two intermediate asymptotic similarity regimes, where the shock wave propagates outwards according to two self-similar laws, initially accelerating and eventually decelerating and vanishing, leading to a static state. The numerical study allows one to investigate in detail this dynamical problem and its time evolution, verifying and complementing the analytic results on the initial solution, intermediate self-similar laws and static long-term solution.

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