On a Godunov-Type Numerical Scheme for Describing Gas and Dust Components in Star Formation Problems

The paper presents one construction of a Godunov-type method based on the separation of operators describing the work of pressure forces and advective transfer. Separate consideration of advective transfer permits describing the motion of both gas and dust components within the framework of a single numerical scheme. In the case of describing gas dynamics, the work of pressure forces is taken into account at a separate stage, independently of transfer. This permits using the numerical scheme in solving star formation problems, where it is necessary to jointly solve the equations of hydrodynamics and dust motion equations. A piecewise parabolic representation of physical variables in all directions is used to reduce the dissipation of the numerical method. The numerical method has been verified on Riemann problems for a hydrodynamic and dust discontinuity, the Sedov problem of point explosion, and the problem of dust cloud collapse, which have an analytical solution.