Published online by Cambridge University Press: 12 August 2022
This chapter addresses issues arising in the time accurate simulation of unsteady flows. In order to enable accurate simulations of time dependent flows with moving shocks and contact discontinuities, there is a need for higher order accurate time discretization schemes that can preserve the TVD property. Additionally, time dependent calculations are needed for a number of important applications, such as flutter analysis or the analysis of the flow past a helicopter rotor, in which the stability limit of an explicit scheme forces the use of much smaller time steps than would be needed for an accurate simulation. This motivates the “dual time stepping” scheme, in which a multigrid explicit scheme can be used in an inner iteration to solve the equations of a fully implicit time stepping scheme. Such schemes are developed in this chapter.