**3. Computational limitations in DHM**

*Hydrology*

where

θ = ( ) <sup>1</sup>

where

5/3 1/2

<sup>n</sup> <sup>=</sup> <sup>=</sup> (5)

<sup>∂</sup> =− − = <sup>∂</sup> (6)

<sup>∂</sup> =− = <sup>∂</sup> (8)

*t X Xy y* (9)

(7)

(10)

1.486 q h S , z x,y

q K K m , z x,y Z Z ZZ *H Z*

1.486 <sup>K</sup> <sup>h</sup> z x,y

*H S* <sup>=</sup> <sup>=</sup> <sup>∂</sup> + ∂

The symbol S in Eq. 7 indicates the flow direction which makes an angle of

y x tan q / q <sup>−</sup> with the positive x-direction. By assuming the value of m to be

q K , z x,y Z Z *H Z*

∂ ∂ ∂ ∂∂ = + ∂∂ ∂ ∂ ∂ *H HH*

If the momentum term groupings were retained, Eq. 9 can be written as

∂ ∂∂ ∂∂ = ++ ∂∂ ∂∂ ∂ *H HH t x xy y*

S Km Km , ( xx yy ) ( ) ∂ ∂

To maintain continuity in the discussion, while salient aspects of the DHM numerical algorithm are presented here, readers are referred to [10] for a detailed description of the numerical formulation and the input file format. The domain is divided into uniform square grids or cells. For each interior grid, its connectivity with adjacent grids along the North, East, South, and West directions is specified. For grids that are on the boundaries, '0' is specified along the directions that do not have adjacent nodes. The flow equation is solved using the nodal domain integration method. Apart from the grid connectors, at the center of each cell, the required input variables are the roughness value, ground elevation, initial flow depth. The number of inflow

= + ∂ ∂ *x y*

and Kx , Ky are also functions of mx , my respectively.

K K. x y

K KS x y

Two-dimensional DHM is formulated by substituting Eq. 8 into Eq. 1

S

m

5/3 Z 1/2

n

negligible, the diffusion model can be expressed as,

Z fz

Eq. 5 can be rewritten in the general case as

**42**

For modeling flows over large sizes domain, the two primary shortcomings in DHM are


Both these limitations were largely due to the computational resources that were available to the developers in the 1980's. Application of DHM over large flow domains would require using a higher number of nodes in the computational domain, warranting modifications to DHM, as discussed next.
