1、Chapter 2 Equations & Numerical Methods1.1 Governing Equations1.1.1 Confined AquiferThe governing flow equation for confined aquifers is developed from application of the law of mass conservation (continuity principle) to the elemental volume. Continuity is given by:Rate of mass accumulation =Rate o
2、f mass inflow - Rate of mass outflow Integrating the conservation of mass with Darcys Law, the general flow equation in three dimensions for a heterogeneous anisotropic material is derived:Assuming that the material is homogeneous, i.e. K does not vary with position, Equation 2-19 can be written as:
3、If the material is both homogeneous and isotropic, i.e.Kx = Ky = Kz , then Equation 2-21 becomes:or, combining partial derivatives:Using the definitions for storage coefficient, (S =MSs ), and transmissivity, (T = KM), where M is the aquifer thickness, Equation 2-22 becomes:If the flow is steady-sta
4、te, the hydraulic head does not vary with time and Equation2-22 becomes:Equation 2-24 is known as the Laplace equation.1.1.2 Unconfined AquiferIn an unconfined aquifer, the saturated thickness of the aquifer changes with time as the hydraulic head changes. Therefore, the ability of the aquifer to tr
5、ansmit water (the transmissivity) is not constant:For a homogeneous, isotropic aquifer, the general equation governing unconfined flow is known as the Boussonesq equation and is given by:If the change in the elevation of the water table is small in comparison to the saturated thickness of the aquifer, the variable thickness h can be replaced with an average thickness b that is assumed to be constant over the aquifer. Equation 2-26 can then be linearized to the form:
