Self-gravitating Euler-Poisson

This page explains the self-gravitating regime of the Euler-Poisson case. To run the case, follow Run the Euler-Poisson case; this page focuses on what the physics means.

The coupling

Self-gravitating means the gas is its own source of potential. The density sets the right-hand side of the Poisson equation, the Poisson solve returns the gravitational potential, and the potential gradient enters the momentum equation as a body force. Mass and momentum stay conservative; the potential is recomputed each step from the current density.

What to look at

• Energy: the total energy (kinetic plus internal plus potential) is a useful conserved diagnostic.

• The Poisson sign: a self-gravitating potential is attractive, the opposite sign of the repulsive plasma coupling used by the diocotron cases.

Learn more

• Run it: Run the Euler-Poisson case.

• The elliptic side: Poisson equation and Elliptic right-hand side and the aux channel.

• The case in adc_cases: euler_poisson.