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The adaptive-mesh method in the problem of the equilibrium rotation of a barotropic star. (English. Russian original) Zbl 0792.65093

Differ. Equations 27, No. 7, 788-792 (1991); translation from Differ. Uravn. 27, No. 7, 1132-1137 (1991).
The paper deals with the numerical treatment of the classical problem of the equilibrium rotation of self-gravitating fluids. The problem is reduced to a motion integral which corresponds to a stationary rotation, and to two elliptic equations: one for the density distribution inside the star and the other for the gravitational potential distribution in the whole space.
A numerical iterative procedure is suggested using the authors’ method for elliptic problems with free boundaries and the method of adapting grids. As result the a priori unknown free boundary of the star is found as well as the density and gravitational potential at the star’s surface.
The efficiency and accuracy of the algorithm is demonstrated for the case of the classical problem of limiting steady rotation of a gas with polytropic equation of state with \(\gamma=5/3\).

MSC:

65Z05 Applications to the sciences
65N06 Finite difference methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics
85A05 Galactic and stellar dynamics
35Q35 PDEs in connection with fluid mechanics
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