JuliaCon 2026

We consider here specifically the dynamics of self-gravitating astrophysical flows, where the governing equations can be split into the hyperbolic hydrodynamic equations describing the flow and an elliptic Poisson equation describing the gravitational potential. For this problem we show that we can use already existing solvers for elliptic and hyperbolic equations, connect them through a joint hierarchical Cartesian mesh and couple them via their source terms depending on each other's state variables. By performing the coupling of these two systems in this way we obtain a multiphysics solver directly combining efficient solvers for their respective coupled governing equations. This coupling also allows indicators for adaptive mesh refinement to take all state variables of the coupled equations into account, which is also true for time step control. Here we couple Trixi.jl, a high-order discontinuous Galerkin framework for solving hyperbolic conservation laws featuring shock capturing and structure preserving methods, and deal.II, a finite-element library written in C++, on a shared adaptive mesh. We apply the resulting solver to some example problems, including a self-gravitating Sedov blast. Our approach is also extendable to other multiphysics systems following a common Eulerian formulation. By using BinaryBuilder.jl we can provide an accessible way to use and adapt this method and also make our results easily reproducible for other interested people.