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Discretization of Conservation Laws

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Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE,volume 54)

Abstract

Many of the basic equations in atmospheric modeling are based on conservation laws. Conservation of mass constitutes the continuity equation, and conservation of momentum establishes the momentum equations. When conservation properties are present in the continuous equations, the numerical (discrete) counterparts should also have conservative properties. Examples for numerical conservation of vorticity or other state variables can be found in [46, 350]. More generally we want a numerical method to adhere to a structure preservation property. To achieve conservation is paramount for all kinds of numerical methods that try to discretize conservation laws. However, for adaptive methods this often poses an additional challenge.

Keywords

  • Shallow Water Equation
  • Discontinuous Galerkin
  • Volume Scheme
  • Dual Cell
  • Upstream Position

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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© 2006 Springer

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Behrens, J. (2006). Discretization of Conservation Laws. In: Adaptive Atmospheric Modeling. Lecture Notes in Computational Science and Engineering, vol 54. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-33383-5_7

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