AbstractComputational methods are now pervasive in the science of aerodynamics. Because previously existing numerical methods proved inadequate for fluid flow simulations, the emergence of computational fluid dynamics (CFD) as a distinct discipline has sparked the development of an entirely new class of algorithms, and a supporting body of theory, which are the main theme of this chapter. After a review of mathematical models of fluid flow, methods for solving the transonic potential flow equation (of mixed type) are examined. The central part of the chapter discusses the formulation and implementation of shockcapturing schemes for the Euler and NavierStokes equations. The chapter next discusses the merits of the contrasting approaches of finite difference, finite volume, and finite element methods for the treatment of flows in complex geometric domains, together with the treatment of boundary conditions. A detailed presentation of explicit and implicit timestepping schemes for both steady and unsteady flows precedes a discussion of preconditioning and multigrid procedures for accelerating the convergence of steadystate calculations. Highorder methods suitable for conducting unsteady simulations on unstructured grids are also presented. In order to realize the potential benefits of CFD, it is essential to move beyond simulation to aerodynamic (and ultimately multidisciplinary) optimization. The chapter concludes with a discussion of aerodynamic shape optimization via control theory.
