NUMERICAL RESULTS

Continuous projection procedure cont'd

Fig. 5: Cross section of the initial condition for Exner's "dune problem" as defined by Eq. (25)

Kubatko_Ocean_Modelling
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NUMERICAL RESULTS

The DG method outlined above has been applied to a number of problems. In this

section, we show the results for three idealized test cases.

Morphological evolution of a symmetric mound

In this test case, we apply the DG method outlined above to the Exner model introduced

The Exner model is examined in order to verify the numerical method

independently of the hydrodynamic model. It also affords us the opportunity to compare our

numerical results to exact solutions so that we may check the order of convergence of the method.

We solve a problem originally posed by Exner (1925). The problem examines the

evolution of an initially symmetric mound subjected to steady, uni-directional flow with a rigid-

lid assumption for the flow. The initial condition is given as:

z ( x, y, 0) = z0 ( x, y ) = A0 + A1 cos ⎜

where the parameters A0 , A1 , and λ are as defined in Fig. 5 which shows a cross section of the

mound along the x-axis. We take A0 = A1 = 1, λ = 20 in Equation (25) and ζ = 3, Aqf = 1 in Eq.

(10). The flow is assumed to be in the x direction only, and we use periodic boundary conditions,

z ( x = -λ 2 , y ) = z ( x = +λ 2 , y ) and z ( x, y = -λ 2) = z ( x, y = +λ 2) The exact

i.e.

solution is given by Eq. (11).

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