Estimation of aerothermal heating for a thermal protection system with temperature dependent material properties

In this paper the aerothermal heating of a reusable launch vehicle with the material parameters depending on temperature is retrieved. An additional information, necessary for solving the corresponding inverse problem, is taken from the temperature values in the selected point of thermal protection system. Minimization of the constructed functional, defining the error of approximate solution, is executed with the aid of Levenberg–Marquardt method. Whereas the direct problem, needed to be solved in order to determine the value of functional mentioned above, is solved by using the implicit scheme of the finite difference method. In this approach a system composed from three layers is considered, which represents an integrated thermal protection system with material parameters depending on temperature.