Numerical simulation of gravitational instability development and clump formation in massive circumstellar disks using integral characteristics for the interpretation of results - Stoyanovskaya, O.P. (Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), 2016)
Results of numerical simulation of instability development and formation of self-gravitating clumps (embryos of protoplanets) in a thin circumstellar gaseous disk are analyzed and systematized. Numerical experiments are performed using a disk model based on a combination of Smoothed Particle Hydrodynamic (SPH) and Hockney methods to solve Poisson’s equation on a uniform Cartesian grid. It is shown that the process of clump formation can be characterized by an average growth rate of the total mass of fragments in the disk; this rate is strongly dependent on the physical parameters of the disk and is slightly dependent on the parameters of the numerical model. It is confirmed that there exists a range of the disk parameters such that the appearance or absence of clumps in the disk depends on the resolution in use and on the details of the numerical algorithm, whereas beyond this range such a dependence is not observed. It is shown that, for a combination of the SPH method with grid-based method to calculate the gravitational force, it is necessary that the hydrodynamic smoothing length does not exceed the grid cell length, otherwise we obtain the following numerical effects in the solutions: the disk shape becomes a square and an artificial grouping of model particles takes place due to the evolution of pairing (clumping) instability in SPH.