# The Advents of Methods For Aircraft Design Software Development

The specialized aircraft design software implements the discrete adjoint method. We will not present in detail the continuous adjoint method, but give below some of its specific elements:

• the discrete method guarantees the coherence between a finite difference evaluation and the calculated value by solving the discrete adjoint equations. This consistency is not ensured by the continuous adjoint method, even if an identical discretization scheme is used for the analysis calculation and the adjoint calculation;
• the cost of the explicit phase of the continuous adjoint calculation is in practice less than that of the explicit phase of the discrete adjoint method. It is difficult to discuss this type of proposal in general. In practice, for the convective terms, the coding of the derivative of a conventional off-center convective flow comprises several times more operations than the application of this flow to the convective term of the continuous adjoint equation.

## Mathematical problems to aircraft design software developers

The continuous adjoint method poses different mathematical problems to aircraft design software developers that do not pose the discrete method:

1. theoretically, jump terms appear in the part integrations if the computational domain contains discontinuity lines. If one can suppose that the discrete residue is a function C 1 of the aerodynamic field, the discrete method poses no problem of regularity: the variation with the parameters of form of the discrete representation of the discontinuities is regular;
2. for some boundary conditions, the definition of continuous adjoint equations is difficult or impossible (it is impossible to eliminate the derivative of the flow in the calculations defining the adjoint vector);
• the diagram of the discrete adjoint method resulting from the linearization of the initial schema does not necessarily have the dissipative character of the discretization of the continuous equations;
• the continuous adjoint method does not make it possible to calculate the gradient of an integral function placed on a curve located – even partially – within the domain of computation.

This is a problem for classical drag analysis for aircraft design software developers, since shock drag is an integral on an edge located in the computational domain around the shock.

## Optimization and other advents of the method

The advent of the adjunct aircraft software development method has allowed a quantum leap in the development of these methods. The gradient of an aerodynamic function is now available for a limited calculation time, and especially regardless of the number of parameters. Therefore, optimizations based on precise descriptions of the geometric shapes have been made. The implementation of local algorithms coupled with codes for the calculation of sensitivities has become widespread in all research teams and these algorithms have been applied to many configurations: wing profiles, wings, complete geometry of an aircraft.

They have significantly improved the performance of aircraft. In planning aircraft design, recent research work focuses in particular on the link between parameterization and the characteristics of optimization problems. For example, the contribution of designing center specialists to the study of the multimodality of a shape optimization problem on the impact of the geometric description richness of a shape during an optimization.