Nonlinear mathematical model for filling thin-walled shells with nonideal gas (Q1348536)

The author investigates analytically the filling of a spherical shell by gas. It is supposed that the gas is nonideal, the penetrability coefficient depends on density or pressure, and the gas obeys the van der Waals equation of state. The problem is to find the time of filling from the initial pressure to the final pressure. It is found that the gas pressure distribution inside the shell can be approximately described by the solution of an initial-boundary value problem for a nonlinear parabolic equation. Using a small parameter, the author obtains an asymptotic series solution. Thus known results for the ideal gas are generalized to the nonideal gas and to the variable gas penetrability coefficient.