General governing equation for transient, heterogeneous, and anisotropic conditions Specific Storage S s =  V / (  x  y  z  h)

 x  y  z = change in storage OUT – IN = = -  V/  t S s =  V / (  x  y  z  h)  V = S s  h (  x  y  z) tt tt

OUT – IN = = -  V tt

Law of Mass Balance + Darcy’s Law = Governing Equation for Groundwater Flow div q = - S s (  h  t) +R* (Law of Mass Balance) q = - K grad h (Darcy’s Law) div (K grad h) = S s (  h  t) –R*

2D confined: 2D unconfined: Storage coefficient (S) is either storativity or specific yield. S = S s b & T = K b

1D, transient, homogeneous, isotropic, confined, no sink/source term Explicit solution (with stability criterion) Implicit solution

Confined Aquifer t = 0 t > 0 Reservoir Problem 1D, transient

t = 0 t > 0 BC: h (0, t) = 16 m; t > 0 h (L, t) = 11 m; t > 0 datum 0 L = 100 m x IC: h (x, 0) = 16 m; 0 < x < L (represents static steady state) Modeling “rule”: Initial conditions should represent a steady state configuration of heads.

datum 0 L = 100 m x At t = t ss the system reaches a new steady state: h(x) = ((h 2 –h 1 )/ L) x + h 1 h2h2 h1h1 (Eqn W&A)

Explicit Solution

t > 0 Water Balance IN + change in storage = OUT IN OUT +- Convention: Water coming out of storage goes into the aquifer (+ column). Water going into storage comes out of the aquifer (- column). Flow in  Storage Flow out  Storage