Solution of ablation equation with a low degree of asymmetry (Q1115736)

The problem of three-dimensional ablation under the influence of convective or radiative heat transfer is posed in a simplified integrolocal form. A semianalytic solution is proposed. By means of linearization (used only to substantiate the method, not in the computational algorithm), the general problem is reduced to a set of isolated two-dimensional problems for each harmonic of the Fourier series in the circumferential variable. Calculated examples indicate a perfectly finite region of applicability of the method with respect to the degree of asymmetry of the problem. The method can be used to provide an efficient means of calculating the complex problem of ablation and dynamics of a body moving in the atmosphere. For high-frequency oscillations, a simple solution of this (generally very awkward) problem is obtained within the framework of the corresponding asymptotic theories.