2D Euler–Poisson self-gravity

Conservative finite-volume evolution of (ρ, ρu, ρv), with selectable first-order or higher-order TVD hydrodynamics and an optional thresholded barotropic equation of state.

Initial condition

Grid

Finite-volume solver

Hydrodynamics

Gravity

Gravity strength G

Poisson iterations / solve

Threshold equation of state

Enable weak pressure above density threshold

Threshold ρ*

Stiffness K

Exponent γ

Time integration / display

Time step Δt

Simulation steps / frame

Density exposure

Shift hue by speed

Maximum hue shift

initializing…

EOS: p(ρ)=K·max(ρ−ρ*,0)^γ. Below ρ* the flow remains pressureless; above it, pressure resists further compression. The second-order option uses primitive-variable MUSCL reconstruction with an MC limiter, Rusanov interface fluxes, SSP-RK2, and kick–hydro–kick gravity splitting.