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Methods for Unsteady Problems

  • Joel H. Ferziger
  • Milovan Perić

Abstract

In computing unsteady flows, we have a fourth coordinate direction to consider: time. Just as with the space coordinates, time must be discretized. We can consider the time “grid” in either the finite difference spirit , as discrete points in time, or in a finite volume view as “time volumes” . The major difference between the space and time coordinates lies in the direct ion of influence: whereas a force at any space location may (in elliptic problems) influence the flow anywhere else, forcing at a given instant will affect the flow only in the future - there is no backward influence. Unsteady flows are, therefore, parabolic-like in time. This means that no conditions can be imposed on the solution (except at the boundaries) at any time after the initiation of the calculation, which has a strong influence on the choice of solution strategy. To be faithful to the nature of time, essentially all solution methods advance in time in a step-by-step or “marching” manner. These methods are very similar to ones applied to initial value problems for ordinary differential equations (ODEs) so we shall give a brief review of such methods in t he next section.

Keywords

Time Level Euler Method Order Scheme Large Time Step Midpoint Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Joel H. Ferziger
    • 1
  • Milovan Perić
    • 2
  1. 1.Dept. of Mechanical EngineeringStanford UniversityStanfordUSA
  2. 2.Computational DynamicsNürnbergGermany

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