Use of (weighted) essentially non-oscillatory advection schemes in a mesoscale model

Abstract

Plain and weighted essentially non-oscillatory advection schemes (ENO and WENO) are implemented in the atmospheric model METRAS to solve the advective terms in the momentum equations. They are an alternative to the currently used centred differences that are stabilized by a Shapiro filter. For the (W)ENO schemes, two approaches are tested for reconstructing the advective fluxes on an Arakawa-C grid. The resulting four second-order (one filtered and three unfiltered) and two (unfiltered) third-order numerical schemes are tested for three different types of test case, i.e. one type consisting of three idealized density current cases, one case with stationary mountain waves and one case with land–sea breeze combined with mountain–valley wind circulations (LSBM). The results are compared to each other and to results of METRAS with centred differences (CDF). When using uniform grids, one of the (W)ENO schemes is ruled out as it turns out to be unstable. The (W)ENO results as well as the CDF result are altogether plausible. They are very similar for stationary and non-convective situations. For convective situations (case LSBM) the results are spread leading to a multi-numerics ensemble. By comparison of the results of the filtered and unfiltered second-order ENO scheme, it is shown that one reason for the spread is the Shapiro filter. As the filter is only meant to stabilize the solution, it must be assumed that the changes caused by the filter are artificial. A grid with step-wise changes in mesh size tested for the density current identifies some shortcomings in the numerical schemes. On this grid the CDF solution contains a large amount of non-physical oscillation while the (W)ENO schemes show reasonable results. When using the second-order (W)ENO schemes, the total CPU time is not much larger than for the CDF scheme. Therefore, two second-order (W)ENO schemes are recommended for step-wise changes in mesh size. The use of the third-order (W)ENO schemes is not justifiable as they do not provide considerably better results and may need more total CPU time. Copyright © 2006 Royal Meteorological Society