Mathematical model of expanding liquid shell.
The mathematical model of an isothermal expanding process of a liquid shell in the state of weightlessness in spherically symmetric case for incompressible Newton's liquid meeting supplementary requirement of hardening at the certain time is dealt with. The solution of model equations is expressed in the form of dependence from internal shell radius behaviour. is obtained. Function R(t) satisfies a time independent nonlinear ordinary differential equation. Various computational algorithms of this equation solution are suggested based on implicit schemes, schemes of predictor - corrector type and modified explicit scheme. The results of numerical calculations on algorithms suggested are presented. The conclusion about computational algorithm advantage based on an explicit modified scheme is grounded. The analytical solution of a hydrodynamic problem of calculation of speed and pressure fields in an expanding liquid shell is obtained. The direct and inverse problems of liquid shell evolution are formulated. The criterion of admissibility of gas feeding regime is stated. On the basis of the analytical solution of a hydrodynamic problem and this criterion the important for practice recommendations concerning the choice of acceptable conditions of process realization and materials with required rheological properties are formulated. Key words: mathematical model, expanding liquid spherical shell, solving stiff time independent nonlinear systems of ordinary differential equations.