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Mass-conservative reconstruction of Galerkin velocity fields for transport simulations.

Scudeler, Carlotta; Putti, Mario; Paniconi, Claudio (2016). Mass-conservative reconstruction of Galerkin velocity fields for transport simulations. Advances in Water Resources , vol. 94 . p. 470-485. DOI: 10.1016/j.advwatres.2016.06.011.

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Résumé

Accurate calculation of mass-conservative velocity fields from numerical solutions of Richards’ equation is central to reliable surface–subsurface flow and transport modeling, for example in long-term tracer simulations to determine catchment residence time distributions. In this study we assess the performance of a local Larson-Niklasson (LN) post-processing procedure for reconstructing mass-conservative velocities from a linear (P₁) Galerkin finite element solution of Richards’ equation. This approach, originally proposed for a-posteriori error estimation, modifies the standard finite element velocities by imposing local conservation on element patches. The resulting reconstructed flow field is characterized by continuous fluxes on element edges that can be efficiently used to drive a second order finite volume advective transport model. Through a series of tests of increasing complexity that compare results from the LN scheme to those using velocity fields derived directly from the P₁ Galerkin solution, we show that a locally mass-conservative velocity field is necessary to obtain accurate transport results. We also show that the accuracy of the LN reconstruction procedure is comparable to that of the inherently conservative mixed finite element approach, taken as a reference solution, but that the LN scheme has much lower computational costs. The numerical tests examine steady and unsteady, saturated and variably saturated, and homogeneous and heterogeneous cases along with initial and boundary conditions that include dry soil infiltration, alternating solute and water injection, and seepage face outflow. Typical problems that arise with velocities derived from P₁ Galerkin solutions include outgoing solute flux from no-flow boundaries, solute entrapment in zones of low hydraulic conductivity, and occurrences of anomalous sources and sinks. In addition to inducing significant mass balance errors, such manifestations often lead to oscillations in concentration values that can moreover cause the numerical solution to explode. These problems do not occur when using LN post-processed velocities.

Type de document: Article
Mots-clés libres: mass conservation; P₁; galerkin; finite volume method; solute transport Richards’ equation; Larson-Niklasson velocity reconstruction; global mass balance; local mass balance
Centre: Centre Eau Terre Environnement
Date de dépôt: 03 mai 2018 15:16
Dernière modification: 03 mai 2018 15:16
URI: http://espace.inrs.ca/id/eprint/5723

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