A Comparison of the Continuous and Discrete Adjoint Approach to Automatic Aerodynamic Optimization

This paper compares the continuous and discrete adjoint-based automatic aerodynamic optimization. The objective is to study the trade-off between the complexity of the discretization of the adjoint equation for both the continuous and discrete approach, the accuracy of the resulting estimate of the gradient, and its impact on the computational cost to approach an optimum solution. First, this paper presents complete formulations and discretization of the Euler equations, the continuous adjoint equation and its counterpart the discrete adjoint equation. The differences between the continuous and discrete boundary conditions are also explored. Second, the results demonstrate two-dimensional inverse pressure design and drag minimization problems as well as the accuracy of the sensitivity derivatives obtained from continuous and discrete adjoint-based equations compared to finite-difference gradients.