Methods for Unsteady Problems

  • Joel H. Ferziger
  • Milovan PerićEmail author
  • Robert L. Street


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.

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Joel H. Ferziger
    • 1
  • Milovan Perić
    • 2
    Email author
  • Robert L. Street
    • 3
  1. 1.Department of Mechanical EngineeringStanford UniversityStanfordUSA
  2. 2.University of Duisburg-EssenDuisburgGermany
  3. 3.Department of Civil and Environmental EngineeringStanford UniversityStanfordUSA

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