Time step size adaptation for unsteady aerodynamic flow simulations: Application to gust encounter simulations

Abstract

This thesis investigates suitable time integration, error estimation and step size control algorithms for the temporal discretization and approximate solution of the unsteady Euler, Navier-Stokes, and Reynolds-Averaged-Navier-Stokes (RANS) equations. The focus lies on applications with an induced unsteadiness such as gust encounter simulations. Embedded Runge-Kutta methods are used to get an estimate of the temporal discretization error. Based on this error, different adaptation algorithms are used to adjust the time step size. The effect of the time step size adaptation is demonstrated for the gust encounter simulations resulting in small time step sizes during the actual encounter with larger time steps before and afterwards. A new time step size limiter is introduced which uses the information from a rejected step to avoid subsequent rejections. Diagonally implicit Runge-Kutta methods with constant and adaptive time step sizes are investigated and compared to backward difference formulae. To solve the linear systems several iterative solution methods are compared together with a discussion on different stage value predictors which yield suitable initial values for the iterative methods.