𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A linear-stability analysis of the semi-implicit semi-Lagrangian discretization of the fully-compressible equations

✍ Scribed by T. J. Payne

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
128 KB
Volume
134
Category
Article
ISSN
0035-9009

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We give a linear‐stability analysis of the two‐time‐level semi‐implicit discretization of the adiabatic fully‐compressible equations on an f‐plane. Previous work has shown that the scheme is stable with respect to perturbations to a hydrostatic and isothermal basic state if the same time‐implicit weight is used throughout and is greater than ½. In this note, we generalize this result to the case where different time weights are used for different terms. © Crown Copyright 2008. Reproduced with the permission of the Controller of HMSO and the Queen's Printer for Scotland. Published by John Wiley & Sons, Ltd.

📜 SIMILAR VOLUMES

An inherently mass-conserving iterative
An inherently mass-conserving iterative semi-implicit semi-Lagrangian discretization of the non-hydrostatic vertical-slice equations
✍ Thomas Melvin; Mark Dubal; Nigel Wood; Andrew Staniforth; Mohamed Zerroukat 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 758 KB

## Abstract Recently 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) c

Coupling a mass-conserving semi-Lagrangi
Coupling a mass-conserving semi-Lagrangian scheme (SLICE) to a semi-implicit discretization of the shallow-water equations: Minimizing the dependence on a reference atmosphere
✍ J. Thuburn; M. Zerroukat; N. Wood; A. Staniforth 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 379 KB

## Abstract In a recent paper, a conservative semi‐Lagrangian mass transport scheme SLICE has been coupled to a semi‐implicit semi‐Lagrangian scheme for the shallow‐water equations. The algorithm involves the solution at each timestep of a nonlinear Helmholtz problem, which is achieved by iterative

An inherently mass-conserving semi-impli
An inherently mass-conserving semi-implicit semi-Lagrangian discretisation of the shallow-water equations on the sphere
✍ M. Zerroukat; N. Wood; A. Staniforth; A. A. White; J. Thuburn 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 674 KB

## Abstract For the shallow‐water equations on the sphere, an inherently mass‐conserving semi‐Lagrangian discretisation (SLICE) of the continuity equation is coupled with a semi‐implicit semi‐Lagrangian discretisation of the momentum equations. Various tests from the literature (two with analytical

A Semi-implicit Semi-Lagrangian Scheme U
A Semi-implicit Semi-Lagrangian Scheme Using the Height Coordinate for a Nonhydrostatic and Fully Elastic Model of Atmospheric Flows
✍ Luca Bonaventura 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 534 KB

A semi-implicit, semi-lagrangian algorithm suitable for the simulation of the dry, adiabatic, nonhydrostatic atmospheric dynamics is introduced and analysed. Height is used as vertical coordinate, without the customary terrain following normalization, thus resulting in a stable, robust, and efficien