ISOTHERMAL COLLAPSE OF A HOMOGENEOUS GAS BALL WITH SELF-GRAVITATION

E. G. Glinskikh
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki 1983. Вып.2. С. 9-12.

      1-D isothermal spherical symmetry gas flows taking into accout Newton gravity forces are considered. For flows where the velocity is linearly dependent upon radii, an exact solution is obtained assuming that the isothermal sound speed is a power function of time. For this solution, densities and pressures do not depend on radii and the particle motion is a breakup to infinity, or focusing to the symmetry center, or periodic pulsations. Conservative difference schemes are analyzed based on the full .conservatism law; kinetic and gravitational energy balance is checked. Disbalance occurence is due to the time step and leads to the solution perturbation which is confirmed by a comparison of numerical solutions with an exact one. The numerical solution obtained using a difference scheme where the equations are made consistent in such a manner that kinetic and gravitational energies are balanced agree well with the exact one.