Paper presented to the 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Florida, 14-16 July 2014.
Capturing flow discontinuities and calculate energy dissipation across the shock wave correctly are challenging numerical simulation problem. Several highly accurate numerical interpolation schemes are employed to capture the shock waves developing in shear flow in shallow waters for two convective Froude numbers. The simulation starts from a small disturbance to the hyperbolic tangent (TANH) based velocity profile. The subsequent linear and nonlinear development of the shear instabilities are obtained from the numerical simulation using the second-order MINMOD, the third-order ULTIMATE-QUICK and the fifth-order WENO schemes. The computational error is evaluated using progressively smaller grid sizes. The number of nodes over a wave length are /x = /y = 16, 32, 64, 128, 256, and 512. The grid refinement determines the accuracy of the simulation and the order of convergence for each scheme. It also determines the dependence of the wave radiation and energy dissipation on the grid size.