This study is a part of a collaboration between the Department of Geography at our university, the Trondheim branch of the Norwegian Water Resources and Energy Directorate (NVE) and our department. We have studied several reaches of the river Nidelva in Trondheim, and we are also studying sections of the river Gaula, where there may be risk of bank erosion. The Department of Geography has been measuring geometry and sediment information in the river, and the NVE has been measuring water velocities using an ADCP. Our department has done numerical modelling of a section of the river Nidelva, near Stavne Bridge. This has been done using our computer program SSIIM. Additionally, a project student has modelled the same reach using the Flow-3D program. Some results are given below:

Three-dimensional view of the simulated section, where the colours show the water depth. Note the scales are distorted, so that the vertical distances look larger then they are in nature.

Three-dimensional view of the simulated section, where the colours show the horizontal water velocity, computed with SSIIM 2.

Three-dimensional view of the simulated section, where the colours show the horizontal water velocity, computed with Flow-3D.

Computed velocities in one cross-section, shown together with the water depths in colours.

Plan view of grid for SSIIM 2. The 3D grid for SSIIM 2 had 101 544 cells. The grid was unstructured, with varying number of cells over the depth. Maximum number of cells was 18 in the deepest part of the section. In the most shallow parts, the grid had only one cell in the vertical direction. The horizonal size of the cells was about 2-3 meters.

Flow-3D used an orthogonal grid. The results shown here were made with grid cells of 2x2 meters in the horizontal directions and 0.15 meters in the vertical direction. 7 million cells were used, where 547 451 cells were active, or filled with water.

Example of grid in a cross-section. Note the distorted vertical scale.

Example of grid in a longitudinal profile. Note the distorted vertical scale.

Computed velocities from SSIIM 2 in the downstream part of the section. The black vectors are velocities close to the water surface and the gree vectors are velocities close to the bed. The figure shows recirculation zones. The results are obtained with the second order upwind scheme.

Computed velocities from SSIIM 2 in the upstream part of the section. The black vectors are velocities close to the water surface and the gree vectors are velocities close to the bed. The figure shows recirculation zones. The results are obtained with the second order upwind scheme.

Computed velocities from SSIIM 2 in a bend of the section. The black vectors are velocities close to the water surface and the gree vectors are velocities close to the bed. The figure shows the secondary currents in the bend, as the surface and bed vectors points in different directions. The results are obtained with the second order upwind scheme.

SSIIM 2 computed (green) and measured (red) velocities close to the water surface at cross-section 8. The measured values have been smoothed using a three-point average for the magnitude of the velocities and a seven-point average for the directions of the vectors.

Comparision between measured and computed velocities near the water surface at Cross-section no 8. Length is in meters and velocity is in m/s. The Flow-3D results are from Run 9, and the SSIIM results are with the first-order upwind scheme.

The SSIIM 2 run with 101 544 unstructured cells and the second-order upwind scheme had a computational time of 30 minutes on the Njord supercomputing system at our university, where it ran on 16 processors. Using the first-order upwind scheme, the computational time was 4 minutes on the same system. The computational time on a 3 GHz dual-core PC would be about 7 times longer.

*This page was last updated: 20. December 2007*