Numerical Solution of Two-Dimensional Unsaturated Flow Problems Using the Meshless Method
- Chih-Yu Liu (National Taiwan Ocean University) | Cheng-Yu Ku (National Taiwan Ocean University) | Chien-Chung Ke (Sinotech Engineering Consultants, Inc.) | Yan Su (Fuzhou University)
- Document ID
- International Society of Offshore and Polar Engineers
- The 28th International Ocean and Polar Engineering Conference, 10-15 June, Sapporo, Japan
- Publication Date
- Document Type
- Conference Paper
- 2018. International Society of Offshore and Polar Engineers
- unsaturated flow, numerical solution, two-dimensional, the Trefftz method
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- 17 since 2007
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The numerical solution of two-dimensional unsaturated flow problems based on the novel advanced computational meshless method was investigated. The numerical solution was approximated by superpositioning the Trefftz basis functions formulated from independent functions satisfying the governing equation in the cartesian coordinate system. To solve the two-dimensional unsaturated flow problems, this study adopted a linear approximation for the nonlinear Richards equation to model flow in unsaturated soils using the Gardner exponential model. The validity of the proposed method is established in several problems. Results indicate that the proposed method may obtain highly accurate numerical solution for two-dimensional unsaturated flow problems.
In engineering practice, soils encountered are partially saturated. Naturally, the unsaturated zone is the portion of the subsurface above the groundwater table which forms a necessary transition between the atmosphere and groundwater aquifers. Although the flow in the unsaturated zone is not a major natural resource of available groundwater resources, it is the main factor controlling water movement from the land surface to the groundwater table and strongly affecting the recharge of saturated zone. Therefore, the movement of flow in the unsaturated zone is one of the most important elements of the hydrological cycle. Several applications of unsaturated flow problems include seepage in unsaturated embankment dams, nearsurface contaminant transport and groundwater resource. Accordingly, it is necessary to understand the movement of flow in the unsaturated zone of hydrological cycle.
The governing equation describing the movement of flow in unsaturated soil, known as the Richards equation, is highly nonlinear (Richards, 1931). Studies showed that the Richards equation is highly nonlinear due to the high nonlinearity of physical behavior of unsaturated soils. Complicated physical relationships of the unsaturated soil properties can be described using soil-water characteristic curves (SWCC). Several empirical equations have been proposed to curve fit the SWCC (Gardner, 1958; Brooks and Corey, 1964; van Genuchten,1980; Fredlund and Xing, 1994). Because of the high nonlinearity of the Richards equation, analytical solutions may not be directly provided. As a result, modeling flow process in unsaturated soils is usually based on the numerical solutions of the Richards equation. Several numerical methods for modeling unsaturated flow problems in the past decades have been developed (Celia et al., 1990; Miller et al., 2006; Casulli and Zanolli, 2010; Juncu et al., 2012). Mesh-based numerical techniques such as the finite difference method and the finite element method are well documented and typically used to solve the unsaturated flow equation in the past (Liu et al., 2015).
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