The inner 1 AU of protostellar disk is hard to investigate during numerical hydrodynamics simulations because of the strict limitations on the timestep. A special model of central sink cell is developed, which allows for a varying mass transport rate through the sink on the nascent protostar and accounts for accretion bursts that may be triggered in the inner disk. The importance of the central unresolved disk region on the evolution of the entire disk with different viscous alpha-parameters is demonstrated. Formation of dusty rings around the star is analyzed and a possible development of the streaming instability is discussed. I also present a new episodic mode of gravitational fragmentation that can develop in evolved circumstellar disks.
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