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The upwinding method

In: Mathematical and Numerical Modelling of Heterostructure Semiconductor Devices: From Theory to Programming

Author

Listed:
  • E. A. B. Cole

    (University of Leeds, Department of Applied Mathematics)

Abstract

It has already been shown in Chapter 7 that, when using the von Neumann stability analysis on the time-discretisation scheme, the magnitude and direction of the electric field has an important bearing on the stability of the scheme. The upwinding method is a method of discretisation which utilises the “flow” of an influence from neighbouring spatial points. This method has previously been applied to the electron continuity equation by making use of Bernoulli functions, but it will be seen how the method can be generalised to use with the energy transport equation using the C-functions which will be introduced in this chapter.

Suggested Citation

  • E. A. B. Cole, 2009. "The upwinding method," Springer Books, in: Mathematical and Numerical Modelling of Heterostructure Semiconductor Devices: From Theory to Programming, chapter 0, pages 229-245, Springer.
    • Handle: RePEc:spr:sprchp:978-1-84882-937-4_9
    DOI: 10.1007/978-1-84882-937-4_9
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