In the study of partial differential equations, particularly in fluid dynamics, a self-similar solution is a form of solution which is similar to itself if the independent and dependent variables are appropriately scaled. Self-similar solutions appear whenever the problem lacks a characteristic length or time scale (for example, the Blasius boundary layer of an infinite plate, but not of a finite-length plate). These include, for example, the Blasius boundary layer or the Sedov–Taylor shell.[1][2]
- ^ Gratton, J. (1991). Similarity and self similarity in fluid dynamics. Fundamentals of Cosmic Physics. Vol. 15. New York: Gordon and Breach. pp. 1–106. OCLC 35504041.
- ^ Barenblatt, Grigory Isaakovich (1996). Scaling, self-similarity, and intermediate asymptotics: dimensional analysis and intermediate asymptotics. Vol. 14. Cambridge University Press. ISBN 0-521-43522-6.