ADH+NSM (Nutrient Sub Model)
Accurate and efficient numerical modeling of flows initiated by dam and levee failure (DLF) is a critical component of hydraulic as well as water resources engineering because of large increases in the flow volume routed through the water body, wave fronts as well as rapid flooding of the banks. Due to these several concurrent phenomenons DLF problems are particularly challenging when compared to other hydrodynamic flows such as flows forced through tides or river discharge/stage.
Dam and levee failure created flows have typically been modeled using explicit methods. The flows are changing rapidly and so the time step is likely to be small. For many river flow conditions implicit models are preferable since they can take longer time steps. The wavelengths/wave periods captured are long and larger time step results in greater efficiency. It is also advantageous to use unstructured meshes. These can be readily made to accurately fit the domain and with modern grid generators are quick to produce.
ADH uses a Pseudo-Transient Continuation (PTC) based scheme to efficiently and accurately capture hydrodynamics as a result of dam and levee failure. Details about the exact implementation of the scheme can be found in Savant et al. (2010). The implementation was tested on several analytical and real world problems.
Test 1: The first test case is a comparison with a study conducted at the US Army Corps of Engineer Engineering Research and Development Center (1960, 1961). The flume was 121.9 m in length and 1.2 m in width. The flume had a slope of 0.0015. The dam is situated 61 m into the flume. Water is pooled upstream of the dam to a depth of 0.3048 m at the dam face, and the flume section downstream of the dam is dry. Data from the numerical model and the experiment were compared at the locations indicated in Figure 1.
Figure 1 Test Case 1
The numerical mesh consisted of 1,200 elements and 755 nodes. The numerical domain is closed and the upstream and downstream walls are impermeable. The Manning’s n value for the run was set at 0.009 s/m1/3. The initial time step and the maximum time step to be utilized in equation 9 were 0.09 and 0.25 seconds, respectively. Figures 2 (A thru F) shows the test results of time history of the water depths for stations 160, 191, 200, 225, 275 and 345. These station numbers are the distance along the flume in feet as indicated in Figure 5. The time of arrival of the surge wave in the numerical model agrees well with the flume observations.
Figure 2 Results Test 1
For stations 200 and 275, the numerical model predicted results drop off faster in slope than the flume near the end of the run compared to the initial part of the run when the flume and the predicted results fall at the same rate. The biggest difference is seen at station 200. The model captures the drop off in the water level but under predicts the peak depth around 50 seconds into the run.
The downstream stations (225, 275 and 345) compare well but also have some points of difference from the physical results. Overall the numerical results are in close agreement with the observed data. At station 275 the flood wave (surge) arrives approximately 5 seconds prior to the observed surge. The greatest error in the simulated depth of approximately 9% occurs at station 345, but the surge arrives at the same time as the observed surge.
Test 2: The second test case is a comparison with a study referenced in Brufau and Garcia-Navarro (2000). This test case was proposed by the Working Group on Dam Break Flow Modeling of the Concerted Action on Dam Break Modeling (CADAM) project. The flume combines a square reservoir and a 45º bend initially wet channel (Figure 3A). The reservoir and the bend will essentially experience 2-D flow. This is a particularly good test case because both the shock speed of the initial wave and the upstream moving hydraulic jump can be compared.
Figure 3A Test 3 Domain
The reservoir is 2.44 m in length and 2.39 m in width, the length of the straight channel is 4.25 m, and the length of the angle section of the flume is 4.15 m. The width of both sections is 0.495 m. Initial water depth in the reservoir is 0.25 m and the channel has an initial depth of 0.01 m. The Manning’s n value reported in the study for the flume bottom and the side walls were 0.0095 and 0.0195 s/m1/3, respectively. The computational mesh consisted of 8,150 elements and 4,316 nodes. The initial and the maximum time step size for use with equation 9 were 0.009 and 0.25 sec, respectively.
Observations were made at 9 points inside the flume (Figure 3B). Comparisons are shown for locations P1, P2, P3, P4, and P5 (Figure 4 A thru E). Other locations show similar behavior. In general, the figures indicate good agreement between the ADH predicted and observed depths and shock speeds. Experimental data show high frequency oscillations which can not be captured by means of the 2D shallow water equations with the hydrostatic assumption Stations P2 and P3 show excellent agreement between the observed wave reflected at the bend and the ADH predicted wave celerity and depth.
Figure 3B Observation Points
Figure 4 Test Case 2 Results
Test 3: The Malpasset dam failed explosively on December 2, 1959. The resulting flood wave was approximately 40m high and resulted in 433 casualties and destroyed infrastructure in the inundated infrastructure including three transformers (A,B,C in figure 5). The time of failure of these transformers are known and will be utilized along with other observed data to validate the performance of the PTC-SER-ADH and ADH models.
Figure 5 Malpasset Dam Break ADH Domain
The failure of the dam and the wave propagation has been widely studied to determine the maximum water surface elevations reached due to the flood wave. These maximum water surface elevations are numbered P1 to P17. In addition experimental data is available from a scaled physical model built at Laboratoire National d’Hydraulique in 1964. The scale factor of the undistorted model is 1:400. The observations from this model are numbered S6-S14 with S1-S5 located in the reservoir.
The mesh constructed to simulate this dam failure consisted of approximately 30,000 nodes and 60,000 elements with a higher resolution provided in the narrow valley (figure 6). The valley below the dam is considered completely dry and the water surface elevation behind the dam is assumed to be 100m. These conditions have been utilized by several researchers and have provided accurate results of the flood wave and the water surface elevations (Valiani et al, 2002 and Schwanenberg, 2004). A constant Manning’s n value of 0.025 s/m1/3 for the entire domain is utilized. Sensitivity runs with Manning’s n values of 0.010 and 0.033 s/m1/3 were also performed, but a value of 0.025 s/m1/3 provided the most accurate results. Table 1 lists the simulated water surface elevations obtained from PTC-SER-ADH and ADH as well as the observed water surface elevations. Table 2 provides the travel time of the flood wave to the transformers.
Figure 6 Mesh Resolution
Table 1 Depth of Water Observed Vs ADH, Table 2 Travel Time to Transformers
For more information, contact the project lead, Gaurav Savant, U.S. Engineer Research and Development Center (ERDC), Coastal and Hydraulics Lab (CHL) at: