Selfsemilar solutions of hydrodynamic equations for expanding layer with boundary condition specified by differential equation
Abstract
A set of self similar solutions of the hydrodynamic differential equations are derived for an expanding layer. The equations consist of continuity, momentum and energy equations. Energy is supplied into the layer constantly in time and homogeneously in space. One end surface of the layer is fixed in the space and the motion of the other end is specified by a partially differential equation. By using a similar variable, the equations are transformed to a set of ordinary differential equations. Forms of these ordinary differential equations and hence the self similar solutions are not unique according to the choice of similar variables. However, the solutions themselves as functions of time and space are unique.
 Publication:

Symposium on Mechanics for Space Flight
 Pub Date:
 March 1983
 Bibcode:
 1983msf..symp....1M
 Keywords:

 Boundary Conditions;
 Boundary Value Problems;
 Density Distribution;
 Inertial Confinement Fusion;
 Ion Beams;
 Partial Differential Equations;
 Equations Of Motion;
 Mach Number;
 Pressure Effects;
 RungeKutta Method;
 SpaceTime Functions;
 Temperature Effects;
 Fluid Mechanics and Heat Transfer