Comparison of TVD and WENO schemes in the case of wave packet transport and vortex numerical diffusion problems

In the given paper, dissipative properties of TVD and WENO schemes are tested and compared. A brief review of limiters used in TVD schemes is presented. An iterative procedure of limiting minmod reconstruction is described. A procedure of WENO-reconstruction inside the cell for uniform grids is presented. For the test cases, a problem of wave packet transport and a problem of numerical diffusion of vortices are used. A problem of wave packet transport is solved for uniform and non-uniform grids. On the basis of comparison of theoretical and numerical solutions, dissipative properties of different limiters for TVD scheme and WENO scheme are estimated.