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| Titel |
A tentative of interpreting Richards' Equation in media with high heterogeneity by Filippov theory |
| VerfasserIn |
Marco Berardi, Fabio Difonzo, Maria Clementina Caputo, Lorenzo De Carlo, Michele Vurro |
| Konferenz |
EGU General Assembly 2016
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| Medientyp |
Artikel
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| Sprache |
en
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 18 (2016) |
| Datensatznummer |
250135809
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| Publikation (Nr.) |
 EGU/EGU2016-16716.pdf |
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| Zusammenfassung |
| The numerical solution of Richards’ equation is accomplished by means of method of lines,
that typically allows the spatial derivative to be approximated by some finite element scheme,
in such a way that any solver for ODEs can be used. The ψ-based form is used,
i.e.
[ ( )]
∂ψ- ∂-- ∂ψ-
C(ψ) ∂t = ∂z K (ψ) ∂z − 1 ,
(1)
for suitable choices of hydraulic capacity function C and hydraulic conductivity function K.
The real challenge is modelling the infiltration at the interface between two media with
high heterogeneity. The interface between two layered media with very different
characteristics can be handled as a discontinuity surface. The effort is to review this case as a
differential system with discontinuous right-hand side and to clarify the meaning of crossing
and sliding in this context, according to Filippov theory. For our scopes, the temporal
derivative has been approximated by means of a finite difference method in such a way
that the numerical integration is accomplished with respect to the spatial variable
z in (1): this choice is particularly convenient since it allows to have a Filippov
system, with a state-dependent threshold, and to have a possible sliding behavior. |
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