2-D stationary gas dynamics in a barred galaxy

A code for solving the 2-D isothermal Euler equations of gas dynamics in a rotating disc is presented. The gravitational potential represents a weak bar and controls the flow. A damped Newton method solves the second-order upwind discretisation of the equations for a steady-state solution, using a consistent linearisation and a direct solver. Successive grid refinement, starting from a finite-volume grid with 8 by 8 cells, is applied to find solutions on subsequently finer meshes. On coarser meshes, a first-order spatial discretisation is used. The method obtains quadratic convergence once the solution approaches the steady state. The initial search is quick with the first-order scheme and slower with the second-order discretisation, up to 256 by 256 cells. Beyond, with 512 by 512 cells, the number of iterations becomes too large to be of practical use. Potential causes are discussed. The code can be applied as a tool for generating flow models if used on not too fine meshes.