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Astron. Astrophys. 347, 442-454 (1999)

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5. The code

For solving the multi-component hydrodynamical Eqs. (6)-(12) we use a second order Van Leer advection scheme as implemented by Stone & Norman (1992) in a general purpose fluid dynamics code, called ZEUS-2D. This code was designed for modeling astrophysical systems in two spatial dimensions, and can be used for simulations of a wide variety of astrophysical processes. The ZEUS-2D code uses sufficiently accurate hydrodynamical algorithms which allow to add complex physical effects in a self-consistent fashion. This code provides therefore a good basis for the implementation of the nonlinear mass transfer processes into the multi-phase hydrodynamics.

The Eulerian codes with the Van Leer advection scheme were successfully used for the investigation of the stability of self-gravitating disks (Laughlin & Róyczka 1996, Laughlin et al. 1997, 1998). The main difference between the "standard" ZEUS-type codes and our one is the introduction of mass and momentum interchange processes between different components. These processes can be computed at the first sub-step of the ZEUS-type code which makes a generalization of the ZEUS-type code straightforward.

Briefly, the code solves the hydrodynamical equations using equally spaced azimuthal zones and logarithmically spaced radial zones. For the simulations discussed here we mainly employed a grid with [FORMULA] cells. To advance the solutions due to interchange processes given by the right-hand sides of the Eqs. (6)-(8) we used the fifth order Cash-Karp Runge-Kutta routine with the time step limitation imposed by the Courant-Friedrichs-Levy criterion and the values of the parameters [FORMULA] and [FORMULA] in mass and momentum interchange processes. The Poisson equation is solved by applying the 2D Fourier convolution theorem in polar coordinates.

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© European Southern Observatory (ESO) 1999

Online publication: June 30, 1999