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Jul 24 2012

One-Dimensional Versus Two-Dimensional Modeling

Continuing with our coverage of the new HDS 7 manual from FHWA.

One-dimensional modeling requires that variables (velocity, depth, etc.) change predominantly in one defined direction, x, along the channel. Because channels are rarely straight, the computational direction is along the channel centerline. Two-dimensional models compute the horizontal velocity components (Vx and Vy) or, alternatively, velocity vector magnitude and direction throughout the model domain. Therefore, two-dimensional models avoid many assumptions required by one-dimensional models, especially for the natural, compound channels (free-surface bridge flow channel with floodplains) that make up the vast majority of bridge crossings over water. Chapters 5 and 6 include detailed discussions of one- and two-dimensional model assumptions and limitations.

Wisconsin River

If the hydraulic engineer has great difficulty in visualizing the flow patterns and setting up a one-dimensional model that realistically represents the flow field, then two-dimensional modeling should be used.

The advantages of two-dimensional modeling include a significant improvement in calculating hydraulic variables at bridges. Therefore FHWA has a strong preference for the use of two-dimensional models over one-dimensional models for complex waterway and/or complex bridge hydraulic analyses. One-dimensional models are best suited for in-channel flows and when floodplain flows are minor. They are also frequently applicable to small streams. For extreme flood conditions, one-dimensional models generally provide accurate results for narrow to moderate floodplain widths. They can also be used for wide floodplains when the degree of bridge constriction is small and the floodplain vegetation is not highly variable. In general, where lateral velocities are small one-dimensional models provide reasonable results. Avoiding significant lateral velocities is the reason why cross section placement and orientation are so important for one-dimensional modeling. Two-dimensional models generally provide more accurate representations of:

· Flow distribution

· Velocity distribution

· Water Surface Elevation

· Backwater

· Velocity magnitude

· Velocity direction

· Flow depth

· Shear stress

Although this list is general, these variables are essential information for new bridge design, evaluating existing bridges for scour potential, and countermeasure design. The Federal Emergency Management Agency (FEMA) also depends on numerical hydraulic models of extreme events to determine flood hazards. FEMA and NOAA (National Oceanic and Atmospheric Administration) commissioned the National Research Council (NRC 2009) to investigate the factors that affect flood map accuracy and identify ways of improving flood mapping. Among their findings, the NRC recommended greater use of two-dimensional models.

Two-dimensional models should be used when flow patterns are complex and one-dimensional model assumptions are significantly violated. If the hydraulic engineer has great difficulty in visualizing the flow patterns and setting up a one-dimensional model that realistically represents the flow field, then two-dimensional modeling should be used. One study that developed criteria for selecting one- versus two-dimensional models is “Criteria for Selecting Hydraulic Models“. The recommendations from that study are summarized and expanded on below.

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