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114 5 2D Shallow-Water Modellingwhere h is layer thickness. The discretised form of the diffusion term for u has thecomponents:A hhA hh⎡ ((∂h ∂u )= A h⎣ h e∂x ∂x h u Δx⎡ ((∂h ∂u )= A h⎣ h n∂y ∂y h u Δy))u n j,k+1 − un j,kh w(u n j,k − ⎤un j,k−1−⎦ (5.34)ΔxΔx))u n j+1,k − un j,kh s(u n j,k − ⎤un j−1,k−⎦ (5.35)ΔyΔywhere layer thicknesses of the faces of the control volume (see Fig. 5.16) are givenby:h u = 0.5 ( h n j,k + )hn j,k+1h e = h n j,k+1h w = h n j,kh n = 0.25 ( h n j,k + hn j,k+1 + hn j+1,k + )hn j+1,k+1h s = 0.25 ( h n j,k + hn j,k+1 + hn j−1,k + )hn j−1,k+1The diffusion terms for v are constructed in a similar fashion.Fig. 5.16 Illustration of locations of layer-thickness h and u grid points for the discretisation ofthe horizontal diffusion terms for u