Jacek A. Jankowski and Andreas Malcherek.

Developing an advection scheme for Telemac-2D based on the 2nd order characteristics method, 8th Telemac User Club, Chatou, 15-16 November 2001.

One of the best method of improving the accuracy of the advection scheme based on method of characterictics is to improve the interpolation of advected variables on the feet of the traced-back characteristic curves. The results of applying the second order interpolation in broader element patches are compared with the presently applied single-element linear interpolation and the SUPG method. The second order interpolation delivers considerable improvements in accuracy due to the diminished numerical diffusion of the scheme, which is demonstrated with the rotating cone test and a few less academic examples, like a hydraulic jump or a river model.

However, in irregular elements the monotony of the scheme is not preserved (over- and undershoots of the values appear) and some treatment of this situation is necessary. Clipping the values and/or switching back to the linear interpolation are discussed. Additionally, in boundary elements only the linear interpolation is applicable. This limits presently the application of the scheme and requires further work or changing the mesh generation constraints, which is explained with a real-world river flow model.

Transparencies are available.