Effect of Friction on Spurious Oscillations in Open Channel Modeling with Variable Bathymetry or Roughness

Abstract

Numerical issues for the friction-dominated steady-state Saint-Venant equations with a shock-capturing upwind finite-element scheme are studied using nonuniform-flow test cases and Fourier analysis. The friction-dominated case is a common phenomenon in open channel flow modeling when the depth becomes small compared with the discretization length. In the nonuniform-flow test cases, abrupt slope changes and abrupt roughness changes are introduced, and in the Fourier analysis, a periodic bed perturbation is used. Nondimensional parameter groups identified are as follows: the upwinding coefficient, the number of elements per wavelength, the average-flow Froude number, and the numerical friction number. The results show that errors in both depth and discharge variables are observed whenever there is any perturbation in the bed topography or bed roughness. These errors increase with increasing Froude number and increasing numerical friction number. A combined friction parameter is introduced for practical application. The combined friction parameter can be used to specify minimum depths or to guide mesh refinement. The analysis framework developed can also be used for other numerical schemes.