Open-source high-performance software packages for direct and inverse solving of horizontal capillary flow
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Abstract
This work introduces Fronts, a set of open-source numerical software packages for nonlinear horizontal capillary-driven flow problems in unsaturated porous media governed by the Richards equation. The software uses the Boltzmann transformation to solve such problems in semi-infinite domains. The scheme adopted by Fronts allows it to be faster and easier to use than other tools, and provide continuous functions for all involved fields. The software is capable of solving problems that appear in hydrology, but also in other particular domains of interest such as paper-based microfluidics. As the first known open-source implementation to adopt this approach, Fronts has been validated against analytical solutions as well as existing software achieving remarkable results in terms of computational costs and numerical precision, and is meant to aid the study and modeling of capillary flow. Fronts can be freely downloaded and installed, and offers a friendly environment for new users with its complete documentation and tutorial cases.
Document Type: Original article
Cited as: Gerlero, G. S., Berli, C. L. A., Kler, P. A. Open-source high-performance software packages for direct and inverse solving of horizontal capillary flow. Capillarity, 2023, 6(2): 31-40. https://doi.org/10.46690/capi.2023.02.02
Keywords
References
Alastal, K., Ababou, R. Moving multi-front (MMF): A generalized Green-Ampt approach for vertical unsaturated ows. Journal of Hydrology, 2019, 579: 124184.
Andersen, P. Ø. Insights from Boltzmann transformation in solving 1D counter-current spontaneous imbibition at early and late time. Advances in Geo-Energy Research, 2023, 7(3): 164-175.
Asadi, H., Pourjafar-Chelikdani, M., Khabazi, N. P., et al. Quasi-steady imbibition of physiological liquids in paper-based microfluidic kits: Effect of shear-thinning. Physics of Fluids, 2022, 34(12): 123111.
Bear, J., Cheng, A. H. D. Modeling groundwater flow and contaminant transport, in Theory and Applications of Transport in Porous Media, edited by Bear, J., Springer, Dordrecht, pp. 89-103, 2010.
Bezanson, J., Edelman, A., Karpinski, S., et al. Julia: A fresh approach to numerical computing. SIAM Review, 2017, 59(1): 65-98.
Braddock, R. D., Parlange, J. Y. Some accurate numerical solutions of the soil-water diffusion equation. Soil Science Society of America Journal, 1980, 44(3): 656-658.
Brooks, R. H., Corey, A. T. Hydraulic properties of porous media. Fort Collins, Colorado State University, 1964.
Bruce, R. R., Klute, A. The measurement of soil moisture diffusivity. Soil Science Society of America Journal, 1956, 20(4): 458-462.
Boltzmann, L. To integrate the diffusion equation with variable diffusion coefficients. Annalen der Physik, 1894, 289(13): 959-964. (in German)
Caviedes-Voullième, D., García-Navarro, P., Murillo, J. Verification, conservation, stability and efficiency of a finite volume method for the 1D Richards equation. Journal of Hydrology, 2013, 480: 69-84.
Chen, X., Dai, Y. An approximate analytical solution of Richards’ equation. International Journal of Nonlinear Sciences and Numerical Simulation, 2015, 16(5): 239-247.
Evangelides, C., Arampatzis, G., Tzimopoulos, C. Estimation of soil moisture profile and diffusivity using simple laboratory procedures. Soil Science, 2010, 175(3): 118-127.
Farthing, M. W., Ogden, F. L. Numerical solution of Richards’ equation: A review of advances and challenges. Soil Science Society of America Journal, 2017, 81(6): 1257-1269.
Feldt, R. BlackBoxOptim.jl. GitHub 2022.
Fritsch, F. N., Butland, J. A method for constructing local monotone piecewise cubic interpolants. SIAM Journal on Scientific and Statistical Computing, 1984, 5(2): 300-304.
Fuentes, C., Haverkamp, R., Parlange, J. Y. Parameter constraints on closed-form soilwater relationships. Journal of Hydrology, 1992, 134(1-4): 117-142.
Gerlero, G. S., Kler, P. A., Berli, C. L. A. Fronts.jl. GitHub 2022a.
Gerlero, G. S., Valdez, A. R., Urteaga, R., et al. Validity of capillary imbibition models in paper-based microfluidic applications. Transport in Porous Media, 2022b, 141(2): 359-378.
Hammond, G. E., Lichtner, P. C., Mills, R. T. Evaluating the performance of parallel subsurface simulators: An illustrative example with PFLOTRAN. Water Resources Research, 2014, 50(1): 208-228.
Hayek, M. An efficient analytical model for horizontal infiltration in soils. Journal of Hydrology, 2018, 564: 1120-1132.
Horgue, P., Renard, F., Gerlero, G. S., et al. porousMulti-phaseFoam v2107: An open-source tool for modeling saturated/unsaturated water flows and solute transfers at watershed scale. Computer Physics Communications, 2022, 273: 108278.
Klute, A. A numerical method for solving the flow equation for water in unsaturated materials. Soil Science, 1952, 73(2): 105-116.
Lai, W., Ogden, F. L. A mass-conservative finite volume predictor-corrector solution of the 1D Richards’ equation. Journal of Hydrology, 2015, 523: 119-127.
Lauwens, B. ResumableFunctions: C# sharp style generators for Julia. Journal of Open Source Software, 2017, 2(18): 400.
Li, Q., Ito, K., Wu, Z., et al. COMSOL Multiphysics: A novel approach to ground water modeling. Groundwater, 2009, 47(4): 480-487.
List, F., Radu, F. A. A study on iterative methods for solving Richards’ equation. Computational Geosciences, 2016, 20: 341-353.
Lomeland, F. Overview of the LET family of versatile correlations for flow functions. Paper SCA2018-056 Presented at International Symposium of the Society of Core Analysts, Trondheim, Norway, 27-30 August, 2018.
Mathias, S. A., Sander, G. C. Pseudospectral methods provide fast and accurate solutions for the horizontal infiltration equation. Journal of Hydrology, 2021, 598: 126407.
Meurer, A., Smith, C. P., Paprocki, M., et al. SymPy: Symbolic computing in Python. PeerJ Computer Science, 2017, 3: e103.
Parlange, J. Y., Barry, D. A., Parlange, M. B., et al. Sorptivity calculation for arbitrary diffusivity. Transport in Porous Media, 1994, 15: 197-208.
Parlange, J. Y., Braddock, R. D. An application of Brutsaert’s and optimization techniques to the nonlinear diffusion equation: The influence of tailing. Soil Science, 1980, 129(3): 145-149.
Philip, J. R. Numerical solution of equations of the diffusion type with diffusivity concentration-dependent. Transactions of the Faraday Society, 1955, 51: 885-892.
Philip, J. R. General method of exact solution of the concentration-dependent diffusion equation. Australian Journal of Physics, 1960, 13: 1.
Prevedello, C. L., Loyola, J. M., Reichardt, K., et al. New analytic solution of Boltzmann transform for horizontal water infiltration into sand. Vadose Zone Journal, 2008, 7(4): 1170-1177.
Rackauckas, C., Nie, Q. Differential equations. jl-a performant and feature-rich ecosystem for solving differential equations in Julia. Journal of Open Research Software, 2017, 5(1).
Revels, J., Lubin, M., Papamarkou, T. Forward-mode automatic differentiation in Julia. arXiv preprint, 2016, 1607: 07892.
Richards, L. A. Capillary conduction of liquids through porous mediums. Physics, 1931, 1(5): 318-333.
Schaumburg, F., Urteaga, R., Kler, P. A., et al. Design keys for paper-based concentration gradient generators. Journal of Chromatography A, 2018, 1561: 83-91.
Shanmugam, M., Kumar, G. S., Narasimhan, B., et al. Effective saturation-based weighting for interblock hydraulic conductivity in unsaturated zone soil water flow modelling using one-dimensional vertical finite-difference model. Journal of Hydroinformatics, 2020, 22(2): 423-439.
Šimůnek, J., Van Genuchten, M. T., Šejna, M. Recent developments and applications of the HYDRUS computer software packages. Vadose Zone Journal, 2016, 15(7): vzj2016.04.0033.
Su, L., Wang, Q., Qin, X., et al. Analytical solution of a one-dimensional horizontal-absorption equation based on the Brooks-Corey model. Soil Science Society of America Journal, 2017, 81(3): 439-449.
Sun, J., Li, Z., Furtado, F., et al. A microfluidic study of transient flow states in permeable media using fluorescent particle image velocimetry. Capillarity, 2021, 4(4): 76-86.
Taylor, J. R. Introduction To Error Analysis: The Study of Uncertainties in Physical Measurements. New York, USA, University Science Books Mill Valley, 1997.
Tzimopoulos, C., Evangelides, C., Arampatzis, G. Explicit approximate analytical solution of the horizontal diffusion equation. Soil Science, 2015, 180(2): 47-53.
Van Genuchten, M. T. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America journal, 1980, 44(5): 892-898.
Villarreal, R., Lozano, L. A., Melani, E. M., et al. Diffusivity and sorptivity determination at different soil water contents from horizontal infiltration. Geoderma, 2019, 338: 88-96.
Virtanen, P., Gommers, R., Oliphant, T. E., et al. SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods, 2020, 17(3): 261-272.
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