Computation of shallow wakes with the fractional step finite element method

The depth-integrated shallow-water equations are used to simulate shallow wake flow around a solid plate-like obstacle. Influences of different terms in the equations are analyzed by normalizing the momentum equation. A fractional step finite element method is used to discretize the shallow-water equations with third-order accuracy and uniform Courant-Friedrichs-Lewy (CFL) property. The established numerical model is used to simulate the shallow wake in three typical cases and the computational flow fields are compared with digital Particle Image Velocimetry (PIV) measurements and flow visualization pictures. Three turbulence models are considered: The results of the standard k-epsilon model agree with the experimental results better than those of zero equation and sub-depth scale turbulence models. Furthermore, the results of the simulation also show that it is the wake stability parameter that mainly controls the flow patterns of shallow wakes.