# Two-Dimensional Flow

In the previous chapters, we considered one-dimensional flows. However, the assumption of one-dimensional flow may not be valid in many situations — e.g., flow in a non-prismatic channel (i.e., channel with varying cross section and alignment), flow downstream of a partially breached dam, or lateral flow from a failed dyke. Although flow in these situations is three-dimensional, we may simplify their analysis by considering them as two-dimensional flows by using vertically averaged quantities. Such an assumption not only simplifies the analysis considerably but yields results of reasonable accuracy.

In this chapter, we discuss the analysis of two-dimensional flows. First, we derive the equations describing unsteady two-dimensional flows. Then, we present explicit and implicit finite difference methods for their solution.

## Keywords

Shallow Water Equation Discontinuous Galerkin Method Bottom Slope Riemann Solver Channel Bottom
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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