# Difference between revisions of "Kees' assignment"

## 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

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