An analytical method for solving the problem of unshocked conical gas compression

The two-dimensional unsteady self-similar problem of unlimited unshocked co nical compression of a gas is investigated. A solution is constructed in th e form of a characteristic series in the domain bounded by a weak discontin uity and the sonic perturbation front. A recursion system of ordinary diffe rential equations is obtained for the coefficients. A boundary-value proble m corresponding to the next approximation is investigated in detail, a fund amental system of solutions is found by analytical methods and its asymptot ic behaviour is investigated. Essentially independent solutions are determi ned and different methods are used to seek a solution of the inhomogeneous equation with the required asymptotic behaviour. An algorithm is constructe d to compute gas flows induced by the motion of a piston taking the first t erms of the series into consideration. The results are compared with those of computations carried out using the method of characteristics. (C) 1999 E lsevier Science Ltd. All rights reserved.