A method for computing selfgravitating gas flows with radiation

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We present a numerical method which is suitable for calculating selfgravitating gas flows including thermodynamic processes and radiation. Such problems arise for example in connection with the formation of new stars by gravitational collapse of interstellar clouds. A particularly difficult problem which must be numerically solved in a consistent way is the settling of matter from a supersonic flow into a hydrostatic equilibrium after passing through a strong shock front. Because this must be done without continuously exciting spurious oscillations with extremely small time scales, very stringent constraints are imposed upon the method of solution. Technically, the method here described incorporates a freely moving coordinate system with a generalized form of Richtmyer's artificial viscosity for smoothing shock fronts (tensor viscosity), the two most important improvements to earlier attempts to solve this problem. The method has been extensively tested for spherically and axially symmetric flows. How to proceed in the full 3D case is briefly outlined. Accuracy problems are discussed in connection with numerical stability. We give examples for collapse, accretion and explosion in spherical symmetry and for collapse and ring formation in an axially symmetric rotating cloud.