Kees' assignment

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Contents

Model equation

\frac{\partial H}{\partial t} = - \frac{\partial}{\partial x}D(x) \frac{\partial H}{\partial x} + M

where

D(x) = C H^{n+2}\frac{\partial h} {\partial x} ^{n-1},

and

C = \frac{2 A}{5} \left(\rho g\right)^n

Model parameters

  • \frac{\partial b}{\partial x} = -0.1
  • M(x) = M_0 - x M_1 = 4 - 2e^{-4} x
  • \rho = 920 kg/m^3
  • g=9.8 m/s^2
  • A = 1e-7  kPa^{-3} a^{-1}

Boundary conditions

  • H_l = 0  (left boundary)
  •  H_r>0 (right boundary)

Numerical tips

Use a staggered grid such that D(x_{j+1/2}), so

D(x_{j+1/2}) = C \frac{1}{2} \left(H_j + H_{j+1}\right)^5 \left(\frac{h_{j+1} - h_j}{\Delta x}\right)^2.

and then the flux will be computed as

-\frac{\partial }{\partial x} H\bar u =