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

The two-dimensional unsteady self-similar problem of unlimited unshocked conical compression of a gas is investigated. A solution is constructed in the form of a characteristic series in the domain bounded by a weak discontinuity and the sonic perturbation front. A recursion system of ordinary differential equations is obtained for the coefficients. A boundary-value problem corresponding to the next approximation is investigated in detail, a fundamental system of solutions is found by analytical methods and its asymptotic behaviour is investigated. Essentially independent solutions are determined and different methods are used to seek a solution of the inhomogeneous equation with the required asymptotic behaviour. An algorithm is constructed to compute gas flows induced by the motion of a piston taking the first terms of the series into consideration. The results are compared with those of computations carried out using the method of characteristics.