Transient reflection of a plane shock wave from a rigid wall

Abstract

In the present study the gas pressure and velocity will be determined, with the assumption that ~p/~x = 0 (on d~e wall this is a consequence of the boundary condition u = 0 and the equations of gasdynamics), from the gasdynamic equations in the form of simple finite formulas with a linearization agreeing with that used in [I]. A numerical solution [2] of the problem of reflection of a strong point discontinuity planar shock wave from a wall using the method of [3] will allow an evaluation of the accuracy of the results obtained and confirm the character of the time dependence of velocity. For large time intervals these relationships are valid in the direct vicinity of the wall. For engineering purposes the formula for determining pressure on the wall obtained in this way is of special interest. Using the results thus obtained, in analogy to [4], the coordinate of the reflected shock front is defined in the form of a section of a Taylor series, which also agrees well with numerical solution. The gasdynamic equations for an ideal gas