Numerical modeling of external 3-D CFD problems on the parallel computers and aerodynamic shape optimization

Abstract

This chapter discusses the development of mathematical models, numerical methods and parallel algorithms for aerodynamic design problems that focus on multiprocessing computing systems. Numerical methods of calculation of 3D flows are considered within the framework of full unsteady Navier-Stokes equations and sub models from the point of view of parallel calculations. Numerical methods are based on a finite-difference, finite-volumes methods, and Godunov's schemes. The codes provide a mathematical modeling of unsteady 3D flows near geometries of the real form. Use of technology of parallel calculations on multiprocessing computer facilities will proceed a qualitatively new approach at the solution of aerodynamic designing problems. One of the basic problems is the grid generation that takes into account geometrical and the physical features of flow field. The physical region is divided into sub-regions and within each sub-region, a structured grid is generated. One method of 3D generation is based on the marching procedure of the parabolic generator. A grid adaptation strategy is included in flow field simulation. Structured meshes are adapted to the flow gradients in boundary layers, wakes, solving the shocks, etc. A grid generation provides a key to the development of numerical methods. The block structured grid generation techniques are based on algebraic interpolation methods and on solution of partial differential equations. The computational fluid dynamics (CFD) problem is solved by a decomposition domain, improving of communication between processors, and with the use of standards of system MPI (message passing interface). Choice of MPI as library is determined according to the requirement, that the resulting program was applicable to various parallel computing platforms. Finally some of results of the CFD applications are displayed. Some solutions of supersonic problems of wing configuration and shape optimization attempts are also considered.