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Arbitrary high order schemes for transport problems

AuthorsLatorre Garcés, Borja ; García-Navarro, Pilar
Keywordshigh order methods
transport problems
Legendre polynomials
passive solute transport
shallow water model
Issue DateJul-2011
CitationNumerical 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)
AbstractIn 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.
Description1 .pdf (8 Pags., 3 Figs.) with the contribution and 1 .pdf file (35 Pags., Figs.) copy of the original powerpoint presentation of the authors.
Appears in Collections:(EEAD) Comunicaciones congresos
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