Boreskov

OP‐2field of the Sun and the field of the disk has been developed. This model describes the basicprocesses at the initial stage of the evolution.The description of gasdynamic processes is carried out in the Eulerian coordinates. Thegoverning equations represent the basic conservation laws. These equations are discretizedwith the numerical method proposed by S. K. Godunov and A. V. Zabrodin [7] for solvinggasdynamic equations in complex geometries on arbitrary moving grids.The whole computational domain is divided into a set of subdomains separated bymoving boundaries. This approach allows us to sufficiently resolve different scales of theproto‐planet disk dynamics. The computational grid consists of 124800 cells in total.The developed numerical model simulates the initial stage of the disk evolution in theRoche’s approximation, when the disc inner field is neglected, and also with taking it intoaccount. The comparison of these two calculations provides data on how the disk innergravitational field influences on the process of the proto‐planet disk evolution.The analysis of the computational results shows that switching on the disk inner fieldchanges the flow structure. Ring‐shaped domains begin to form, in which the flow sodevelops that it results in the mass concentration in certain radial cross‐sections of the disc.This can be clear seen from snapshots of instantaneous streamlines. When the innergravitational field is switched on one can see the formation of several subdomains. The gasin each of these subdomains tends to move to a radial cross‐section, with the density beingincreased near this section. In comparison with the flow without the inner field, the flow insubdomains above the cross‐section lines oppositely changes the direction of motion.The contour lines of density in the proto‐planet disk are changed in accordance with thechange in behavior of the streamlines. In Figs. 1 and 2 density contours are shown at twodifferent time moments. As can be seen, the inner gravitational field causes the flowinstability that develops in the form of the rings of density (Fig. 2). Local maximums andtypical cross‐clamping of contour lines are well‐defined in the density distribution of theproto‐planet disk at the moment t=0.685 (non‐dimensional). The structure of rings isphysically intelligible: appearance of the Jeans instability (i.e., local increase in gas density)leads to local mass concentrations that begin to gravitationally attract surrounding masses ofgas, in consequence of which local maximum and cross‐clamping in contour lines come out.This corresponds to local decrease in the thickness of the proto‐planet disk.32