Advection Problem

  • Lars Petter RøedEmail author
Part of the Springer Textbooks in Earth Sciences, Geography and Environment book series (STEGE)


The purpose of this chapter is to study potentially useful schemes and discretizations of the linear advection equation. We discuss various stable and consistent schemes such as the leap-frog scheme, the upstream scheme (or upwind scheme), the Lax–Wendroff scheme, and the semi-Lagrangian scheme. The conditions under which they are stable are also discussed, along with ways to avoid the initial problem in centered-in-time schemes. We consider problems like numerical dispersion, numerical diffusion, and computational modes, including ways to minimize their effects, and we discuss flux corrective schemes, which improve the ubiquitous numerical diffusion inherent in low-order schemes like the upstream scheme. Finally, we describe the Courant–Friedrich–Levy (CFL) condition and its physical interpretation.


Upstream Scheme Flux Correction Scheme semi-Lagrangian Scheme Numerical Diffusion Leap-frog Scheme 
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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of GeosciencesUniversity of OsloOsloNorway
  2. 2.Norwegian Meteorological InstituteOsloNorway

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