Comparison of the water movement by Richard and Darcy
Simulations of water movement in the soil are pervasive, Darcy’s law, Darcy- Buckingham’s law and Richard’s equation are all approved equations for this purpose. The Richard’s equation is the most reliable model which is introduced by Lewis Richardson who was the first one to propose that Darcy’s law was originally fabricated for flow in the saturated zone while for flow in vadose zone Darcy-Buckingham’s law can be used in case of steady state condition. Since it is impossible in nature for flow to be steady, Richard proposed a highly nonlinear partial differential equation (PDE) equation which a combination of Darcy’s law and continuity equation. Hydraulic conductivity K(LT-1) and moisture content θ (L 3L 3) are two important variables of Richard’s equation. Considering the nonlinearity of its variables Richard’s equation lacks a general closed form solution. For this purpose, many researchers derived numerical and analytical models to solve Richard’s equation. In this paper, Green Ampt Infiltration Equation is presented to solve Richard’s equation which is one of the most widely used analytical methods.
BROWN, G. J. W. R. R. 2002. Henry Darcy and the making of a law. 38, 11-1-11-12.
CHÁVEZ-NEGRETE, C., DOMÍNGUEZ-MOTA, F., SANTANA-QUINTEROS, D. J. C. & GEOTECHNICS 2018. Numerical solution of Richards’ equation of water flow by generalized finite differences. 101, 168-175.
FARTHING, M. W. & OGDEN, F. L. J. S. S. S. O. A. J. 2017. Numerical solution of Richards’ Equation: a review of advances and challenges. 81, 1257-1269.
HILLEL, D. 2012. Soil and water: physical principles and processes, Elsevier.
HOU, X., VANAPALLI, S. & LI, T. J. C. G. J. 2019. Water flow in unsaturated soils subjected to multiple infiltration events.
KOVALCHUK, N. & HADJISTASSOU, C. J. T. E. P. J. E. 2019. Laws and principles governing fluid flow in porous media. 42, 56.
KUNTZ, D. & GRATHWOHL, P. J. J. O. H. 2009. Comparison of steady-state and transient flow conditions on reactive transport of contaminants in the vadose soil zone. 369, 225-233.
KUTILEK, M., NIELSEN, D. & REICHARDT, K. J. T. L. N. C. O. S. P., INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS 2007. Soil water retention curve, interpretation.
LIU, H.-H. Fluid Flow in the Subsurface.
MENZIANI, M., PUGNAGHI, S. & VINCENZI, S. J. J. O. H. 2007. Analytical solutions of the linearized Richards equation for discrete arbitrary initial and boundary conditions. 332, 214-225.
NARASIMHAN, T. J. V. Z. J. 2007. Central ideas of Buckingham (1907): A century later. 6, 687-693.
NAVON, I. M. 2009. Data assimilation for numerical weather prediction: a review. Data assimilation for atmospheric, oceanic and hydrologic applications. Springer.
NIMMO, J. R., HEALY, R. W. & STONESTROM, D. A. J. E. O. H. S. 2005. Aquifer recharge. 4, 2229-2246.
NIMMO, J. R. J. E. O. H. S. 2006. Unsaturated zone flow processes.
OULHAJ, A. A. H., CANCÈS, C. & CHAINAIS-HILLAIRET, C. 2018. Numerical analysis of a nonlinearly stable and positive Control Volume Finite Element scheme for Richards equation with anisotropy.
PINDER, G. F. & CELIA, M. A. 2006. Subsurface hydrology, John Wiley & Sons.
POUR, M. A., SHOSHTARI, M. M. & ADIB, A. J. W. A. S. J. 2011. Numerical solution of Richards equation by using of finite volume method. 14, 1838-1842.
RAWLS, W. J., BRAKENSIEK, D. L. & MILLER, N. J. J. O. H. E. 1983. Green-Ampt infiltration parameters from soils data. 109, 62-70.
SELKER, J. S., MCCORD, J. T. & KELLER, C. K. 1999. Vadose zone processes, CRC Press.
SIMMONS, C. T. J. H. J. 2008. Henry Darcy (1803–1858): Immortalised by his scientific legacy. 16, 1023.
TRACY, F. J. J. O. H. 2007. Three-dimensional analytical solutions of Richards’ equation for a box-shaped soil sample with piecewise-constant head boundary conditions on the top. 336, 391-400.
TRACY, F. J. W. R. R. 2006. Clean two‐and three‐dimensional analytical solutions of Richards' equation for testing numerical solvers. 42.
YUAN, F. & LU, Z. J. V. Z. J. 2005. Analytical solutions for vertical flow in unsaturated, rooted soils with variable surface fluxes. 4, 1210-1218.
ZHANG, Z., WANG, W., YEH, T.-C. J., CHEN, L., WANG, Z., DUAN, L., AN, K. & GONG, C. J. J. O. H. 2016. Finite analytic method based on mixed-form Richards’ equation for simulating water flow in vadose zone. 537, 146-156.
Copyright (c) 2020 Dana khider mawlood, kurdistan neyaz adnan
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
At Zanco Journal, we're dedicated to protecting your rights as an author, and ensuring that any and all legal information and copyright regulations are addressed. Whether an author is published with Zanco Journal or any other publisher, we hold ourselves and our colleagues to the highest standards of ethics, responsibility and legal obligation