On several numerical strategies to solve Richards’ equation in heterogeneous media with finite volumes

Bassetto, Sabrina; Cancès, Clément; Enchéry, Guillaume; Tran, Quang Huy

doi:10.1007/s10596-022-10150-w

Cited by 7 publications

(1 citation statement)

References 53 publications

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“…[1,5]. Regarding spatial discretization we mention continuous Galerkin finite elements [6,7], mixed or expanded mixed finite elements [8,9,10,11,12], finite volumes [13,14] (see also the recent review [15]), or multipoint flux approximation (MPFA) [16]. Regardless of the choice of the spatial discretization method, one has to solve at each time step a nonlinear, finite-dimensional problem.…”

Section: Introductionmentioning

confidence: 99%

An adaptive solution strategy for Richards' equation

Stokke¹,

Mitra²,

Storvik³

et al. 2023

Preprint

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Flow in variably saturated porous media is typically modelled by the Richards equation, a nonlinear elliptic-parabolic equation which is notoriously challenging to solve numerically. In this paper, we propose a robust and fast iterative solver for Richards' equation. The solver relies on an adaptive switching algorithm, based on rigorously derived a posteriori indicators, between two linearization methods: L-scheme and Newton. Although a combined L-scheme/Newton strategy was introduced previously in [1], here, for the first time we propose a reliable and robust criteria for switching between these schemes. The performance of the solver, which can be in principle applied to any spatial discretization and linearization methods, is illustrated through several numerical examples.

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Section: Introductionmentioning

confidence: 99%

An adaptive solution strategy for Richards' equation

Stokke¹,

Mitra²,

Storvik³

et al. 2023

Preprint

View full text Add to dashboard Cite

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Adaptive regularization for the Richards equation

Févotte,

Rappaport,

Vohralík

2024

Comput Geosci

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Modelling sludge dewatering in treatment reed bed considering sludge deposit formation

Huong,

Tan,

Tang

et al. 2024

Model. Earth Syst. Environ.

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The accumulation of sludge deposits is a crucial factor in the dewatering efficiency of sludge treatment reed bed (STRB). This paper presents an improved one-dimensional process-based mathematical model to simulate the dewatering mechanism in STRBs, in which the compressible cake filtration (CCF) theory was implemented to simulate the sludge deposits accumulation on the surface of the reed bed, while the varying sludge deposit thickness was accounted for using the moving mesh method. The proposed model also included the dual porosity variably saturated flow model and the Penman–Monteith equation to describe the dewatering through gravity drainage and evapotranspiration, respectively. The results from the model were validated with experimental data from laboratory-scale STRBs treating septage. The simulation results showed that considering the sludge deposit layer as a specific flow resistance effectively avoids the overprediction of water infiltration rate in the reed bed. The predicted results showed excellent agreement with the actual data, where only five cases of the root mean square error were above 10% compared to the average effluent flux. Further, the effect of evapotranspiration was found to be insignificant within a short-term simulation. The consideration of the influence of sludge deposit formation on drainage dewatering using the CCF model and moving mesh model has delivered a more robust simulation for sludge dewatering in STRBs, and the proposed model is capable of facilitating the understanding of the interactions between the sludge dewatering in STRB with respect to the bed characteristics, hydraulic load, and solid load.

show abstract

On several numerical strategies to solve Richards’ equation in heterogeneous media with finite volumes

Cited by 7 publications

References 53 publications

An adaptive solution strategy for Richards' equation

An adaptive solution strategy for Richards' equation

Adaptive regularization for the Richards equation

Modelling sludge dewatering in treatment reed bed considering sludge deposit formation

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