Computational Geosciences

, Volume 6, Issue 2, pp 123–139 | Cite as

Godunov Mixed Methods on Triangular Grids for Advection–Dispersion Equations

  • A. Mazzia
  • L. Bergamaschi
  • C.N. Dawson
  • M. Putti
Article

Abstract

A time-splitting approach for advection–dispersion equations is considered. The dispersive and advective fluxes are split into two separate partial differential equations (PDEs), one containing the dispersive term and the other one the advective term. On triangular elements a triangle-based high resolution Finite Volume (FV) scheme for advection is combined with a Mixed Hybrid Finite Element (MHFE) technique to solve dispersion. This approach introduces an error proportional to the time step and the overall scheme is only first order accurate if special care is not taken in the definition of the numerical flux approximation for advection. By incorporating the diffusive effects into the definition of this numerical flux, near second order accuracy (up to a log h factor) can be proved theoretically and validated by numerical experiments in both one- and two-dimensional cases.

finite volume mixed hybrid finite element time-splitting transport equation triangular grid 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • A. Mazzia
    • 1
  • L. Bergamaschi
    • 1
  • C.N. Dawson
    • 2
  • M. Putti
    • 1
  1. 1.Dipartimento di Metodi e Modelli Matematici per le Scienze ApplicatePadovaItaly
  2. 2.Texas Institute for Computational and Applied MathematicsThe University of Texas at AustinAustinUSA

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