2024-03-28T16:03:21Zhttp://digital.csic.es/dspace-oai/requestoai:digital.csic.es:10261/917782016-11-24T09:23:30Zcom_10261_75com_10261_6col_10261_454
DIGITAL.CSIC
author
Latorre Garcés, Borja
author
García-Navarro, Pilar
2014-02-14T08:03:38Z
2014-02-14T08:03:38Z
2011-07
Numerical Methods for Hyperbolic Equations: Theory an Appl ications. An international conference to honour Professor E. F. Toro (Santiago de Compostela, Spain. 4-8 july 2011)
http://hdl.handle.net/10261/91778
In this work, a method based on Legendre polynomials is presented for the simulation of the passive transport
of a solute. The formulation is conservative, explicit and made in a single step. The spatial accuracy is achieved
by means of cell polynomial approximations using Legendre series. This kind of spatial representation is also
found in finite element discretization and allows for information on the variation of the fields at the sub-grid
scale. The time resolution of the transport is based on both a numerical estimation of the displacement at the
advection speed and a grid deformation, according to the semi-Lagrangian rules, followed by a projection of
the solution on the fixed initial grid.
First, the resolution of the scalar transport of a concentration field is presented. The main interest is focused on
the analysis of the accuracy and the efficiency of the method when moving from order 1 to order 20 as compared
to standard methods of virtual reconstruction. The interest in this work is the study of the computational saving
that can be achieved if the required accuracy is medium or low. This is possible thanks to the sub-grid information
that offers the possibility to solve problems with enough accuracy using only a few grid cells and high
order polynomials. Furthermore, this enables the use of large time steps hence leading to low computational
times.
In a second part, the method is applied to the resolution of the passive transport of a solute in shallow water
flows. A technique has been developed to couple Legendre schemes to any conservative method used for the
resolution of the shallow water equations. The coupling offers the possibility to combine solvers of different
order of accuracy, always enforcing conservative and monotone behavior in the numerical solution of the solute
concentration. This strategy is interesting since it is possible to require high order of accuracy only in the solute
transport simulation, hence concentrating the computational effort in the component with more numerical error.
The coupled method is applied to solve transport problems including bed level variations (source terms in the
flow equations), water depth discontinuities and different regimes in order to analyze the performance of the
proposed coupling technique.
eng
openAccess
high order methods
transport problems
Legendre polynomials
passive solute transport
shallow water model
Arbitrary high order schemes for transport problems
comunicación de congreso
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