Methods for Unsteady Problems
This chapter is devoted to methods of time integration. First, the methods of solving ordinary differential equations are described, including basic methods, predictor-corrector and multipoint methods, and Runge–Kutta methods. The application of these methods to the generic unsteady transport equation is described next, including analysis of stability and accuracy. Implicit second-order schemes, which are most widely used in commercial CFD-software, are described in detail, including the handling of non-uniform time steps. The features of some basic methods are demonstrated on two examples.