INNOVATIVE AERODYNAMIC DESIGN BASED ON SUPERCOMPUTER TECHNOLOGY

We use a robust, accurate and computationally efficient algorithm of global genetic search for optimal solutions. The algorithm incorporates an innovative strategy of placing non-linear constraints upon the solution. Instead of the traditional approach in which only feasible (that is non-violating constraints of the optimization problem) points are included in a search path, we employ search paths through both feasible and infeasible points. The information comprised in “forbidden” (infeasible) regions may be very important for the search, and the paths which are allowed to cross the infeasible area may be substantially shorter. We construct an extension of the fitness function by evaluating it at infeasible points. This can be implemented due to a basic property of Genetic Algorithms (GAs): contrary to classical optimization methods, GAs are not confined to only smooth extensions of objective function.

Classical Genetic Algorithms possess a low computational efficiency where the evaluation of the cost function is computationally expensive. To overcome this, we use a ROM (Reduced-Order-Models) approach in a specially developed form of LAM (Local Approximation Method), in which the solution functionals (such as drag and lift) are approximated by a local database. The database is obtained by solving full Navier-Stokes equations in a discrete neighborhood of the current basic point in the search space. To ensure the global character of the overall search, we perform outer iterations in such a way that the final optimal point of each iteration serves as the initial point for the next one.

One of key difficulties in the implementation of aerodynamic shape optimization is that each numerical test requires a new computational grid. In order to avoid a troublesome manual generation of numerical meshes within the optimization process and to maintain the optimization process continuous, we make use of topological similarity of geometrical configurations, involved in the optimization, and all the required grids are constructed by means of a fast automatic transformation of the initial grid which corresponds to the starting basic geometry.

We have developed a highly scalable parallelization implementation on multiprocessors, which allows for obtaining optimal shapes in limiting deadlines.

The process of optimal design is driven by high-accuracy numerical solutions of the full Navier-Stokes equations.