A semi-implicit unstructured operator-difference scheme for three-dimensional self-gravitating flows

A support operators (operator-difference) method has proven itself well for implicit simulations of different astrophysical fluid flows. Following the operator-difference approach, we construct nodal difference analogues differential in Cartesian coordinates, where conjugacy properties are same as original ones. Using operators, develop an Eulerian semi-implicit gas-dynamical solver with self-gravity on a three-dimensional collocated unstructured tetrahedral mesh. In solver, only acoustic waves treated implicitly, resulting to elliptic equation pressure each time-step. The derived allow us symmetric sign-definite matrices this Poisson gravitational potential. stability condition proposed scheme is milder, than usual Courant-Friedrichs-Lewy explicit solvers, and depends gas velocity. Results test problems' low high Mach number flows presented.