The Design of Steady State Schemes for Computational Aerodynamics

The majority of industrial computational fluid dynamics simulations are steady. Such simulations therefore require numerical methods which can rapidly converge a boundary value problem, typically either the Euler or Reynolds-averaged Navier–Stokes (RANS) equations. In this chapter we outline two major approaches: time-marching methods built on top of Runge–Kutta time-stepping schemes and Newton–Krylov methods. A range of techniques for accelerating convergence are presented including local time-stepping, enthalpy damping, residual averaging, multigrid methods and preconditioning.More recent hybrid approaches such as theRunge–Kutta symmetricGauss–Seidel are also discussed. The effectiveness of these methodologies, within the context of several Euler and RANS test cases, is also evaluated.