Week 6

Question 1

What is a conceptual model?

Answer 1

A diagram to summarise ideas

e.g. “developing an approximate solution for a 1 dimensional groundwater flow equation for a homogenous confined aquifer using the finite difference method”

Question 2

What does discretising in time and space mean?

Answer 2

Creating “pockets” of measure

Question 3

Concept of forward difference approximations

Answer 3

Future - current, to find current

Question 4

Concept of backward difference approximations

Answer 4

Current - past, to find current

Question 5

Finite difference approximation, basic gist

Answer 5

1. Forward difference approximations for
   dh/dt
   dq/dx
2. Darcy’s law and therefore backward difference approximations for
   q(n,i)
   q(n,i+1)
3. Make all substitutions into
   Ss(dh/dt) = -dq/dx
4. Rearrange for h(n+1, i) =
5. Assume uniform spacing between points i.e.

t(n+1)-t(n) = /\t
x(i+1)-x(i) = x(i)-x(i-1)=/\x

6. Form finite difference solution

N.B. Can substitute also:
T = HK
S = Has

Question 6

Stability criterion

Answer 6

(K/\t)/(SS/\x^2) < 1/2

Question 7

How many boundary conditions with you have with Nth order derivatives in time(t) and space(x)?

Answer 7

N number of boundary conditions

Question 8

Type I boundary conditions

Answer 8

aka Dirichlet

Fixed head condition

e.g. h=ho

Question 9

Type II boundary conditions

Answer 9

aka Neumann

Fixed gradient condition

e.g. dh/dx = Jo