The methods for the numerical solution of the dual problem of the flow in the first forum sections means that the jet combustion liquid rocket engine (LRE) , a non-viscous flow of the jet speed blunt body made of carbon material (PA ) on unsteady heating and ablation of the body is described. This technique is used to determine the design of hypersonic vehicles les tatelnyh characterized by significant changes in the external contour of the elements of high-temperature due to their ablation.