Local Aerothermal Optimization Method Based on Discrete Adjoint

Optimal aerothermal shape design benefits performance improvement in hypersonic aircraft, where discrete adjoint-based optimization has superiority. However, it faces several challenges, including derivation of the coefficient matrix, solution of adjoint equations, and deformation of structured grids. This article introduces a differential seed lattice traversing technique to deduce the coefficient matrix explicitly, proposes a Block-LUSGS time-marching method to improve the efficiency of adjoint equations solution, and develops a large local deformation technique for structured grids. Specifically, the proposed optimization method employs the steepest descent technique to determine the optimization direction and the golden ratio method to calculate the optimization step size. Optimization of a sphere flat plate gives an 11.8% reduction in peak heat flux, consistent with expectations. Optimization of a compression corner has a 30.4% reduction in peak heat flux, exceeding expectations. These examples validate the effectiveness of the newly proposed optimization method, showing its significant potential for broader applications.