An inherently mass‐conserving iterative semi‐implicit semi‐Lagrangian discretization of the non‐hydrostatic vertical‐slice equations

Abstract

AbstractRecently an inherently mass‐conserving semi‐Lagrangian transport scheme has been successfully coupled to an iterative semi‐implicit scheme in a global shallow‐water‐equation (SWE) model. Here that methodology is extended and applied to an iterative semi‐implicit semi‐Lagrangian (SISL) compressible, non‐hydrostatic vertical‐slice model, in which the constant reference state of the SWE model is now replaced by a vertically varying reference state. An advantage of this approach is that it preserves the same basic structure as the interpolating, non‐mass‐conserving, iterative SISL model. The resulting mass‐conserving model is applied to a standard set of test problems for such models and compared with results from both the literature and the interpolating, iterative SISL version of the model. © Crown Copyright 2010. Reproduced with the permission of HMSO. Published by John Wiley & Sons, Ltd.