D-R-A-F-T
[T ] = ∫∫ [N ]T [N ]dxdy
D
the steady-state system coefficient matrix [Κ] is
Equation 27
∂N j
∂C ∂N j
∂C ⎤
⎡
^
^
^
^
⎧ ∂C
^⎫+
∂C
[K ] = ∫∫ ⎢ K j ⎨u + v - α 1 C ⎬
+
Dx
Dy
⎥dxdy
∂x
∂y
∂x
∂x ∂y
∂y ⎥
D⎢
⎩
⎭
⎦
⎣
the boundary loadings vector {F} is
Equation 28
{F } = -∫∫ [N ]T { 2}dxdy + ∫ [N ]T {q}dζ
α
ζ
D
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.
Equation 29
⎧[T ]
n+1 ⎫
⎨ + θ [K ] ⎬{C}
n+1
⎩ ∆t
⎭
⎧[T ]
⎫ n
= ⎨ - (1 - θ )[K ]n ⎬{C} + θ {F } + (1 - θ ){F}n
n+1
⎩ ∆t
⎭
Elements Types Supported
Two Dimensional Elements
One-Dimensional Elements
Special Elements
Two Dimensional 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
18 Conceptual Program Design
Users Guide To SED2D-WES
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