[T ] = ∫∫ [N ]T [N ]dxdy

the steady-state system coefficient matrix [Κ] is

∂N j

∂C ∂N j

∂C ⎤

⎡

^

^

^

^

⎧ ∂C

^⎫+

∂C

[K ] = ∫∫ ⎢ K j ⎨*u * + *v * - α 1 C ⎬

+

⎥*dxdy*

∂x

∂y

∂x

∂x ∂y

∂y ⎥

⎩

⎭

⎦

⎣

the boundary loadings vector {*F*} is

{F } = -∫∫ [N ]T { 2}dxdy + ∫ [N ]T {q}dζ

α

ζ

Applying the Crank-Nicholson scheme, where θ is the implicitness coefficient, gives

the following equation, where n refers to the present, n+1 to the future time-step,

and ∆t the computation time interval.

⎧[T ]

⎨ + θ [K ] ⎬{C}

⎩ ∆*t*

⎭

⎧[T ]

⎫ n

= ⎨ - (1 - θ )[*K *]n ⎬{C} + θ {F } + (1 - θ ){*F*}n

⎩ ∆*t*

⎭

Two Dimensional Elements

One-Dimensional Elements

Special Elements

The sediment transport model has always supported the traditional two dimensional

6-noded isoperimetric triangle and 8-noded isoperimetric quadrilateral elements.

These are the same types of elements supported by RMA2.

However, the 2D off-channel storage features within RMA2 are not fully supported

in SED2D WES. There is no concentration book-keeping in the off-channel storage

area in the sediment model.

Rectangular Element

Triangular Element

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