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CSDMS 2023: Patterns and Processes Across Scales

Finite Volume Methods for Surface Dynamics Modeling

Randall LeVeque

University of Washington, United States

Many problems of interest to CSDMS members involve solving systems of conservation laws or balance laws for water wave propagation and inundation, erosion and sediment transport, landscape evolution, or for the flow of overland floods, glaciers, lava, or groundwater. It is often natural to solve these partial differential equations numerically with finite volume methods, in which the domain of interest is divided in finite grid cells and the quantities of interest within each grid cell are updated every time step due to fluxes across the cell boundaries and/or processes within the cell. I will give a brief introduction to some of the general theory of finite volume methods and considerations that affect their accuracy and numerical stability, with illustrations from some of the applications mentioned above.

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Of interest for:
  • Marine Working Group
  • Terrestrial Working Group
  • Coastal Working Group
  • Education and Knowledge Transfer (EKT) Working Group
  • Cyberinformatics and Numerics Working Group
  • Hydrology Focus Research Group
  • Chesapeake Focus Research Group
  • Critical Zone Focus Research Group
  • Human Dimensions Focus Research Group
  • Geodynamics Focus Research Group
  • Ecosystem Dynamics Focus Research Group
  • Coastal Vulnerability Initiative
  • Continental Margin Initiative
  • Artificial Intelligence & Machine Learning Initiative
  • Modeling Platform Interoperability Initiative
  • River Network Modeling Initiative