Well-Posed Lateral Boundary Conditions for Spectral Semi-Implicit Semi-Lagrangian Schemes : Tests in a One-Dimensional Model

The aim of this paper is to investigate the feasibility of well-posed lateral boundary conditions in a Fourier spectral semi-implicit semi-Lagrangian one-dimensional model. Two aspects are analyzed: (i) the complication of designing well-posed boundary conditions for a spectral semi-implicit scheme...

Full description

Saved in:
Bibliographic Details
Published in:Monthly weather review 2009, Vol.137 (1), p.315-330
Main Authors: VOITUS, F, TERMONIA, P, BENARD, P
Format: Article
Language:English
Subjects:
Boundaries
Boundary conditions
Boundary value problems
Buffer zones
Earth, ocean, space
Exact sciences and technology
External geophysics
Iterative methods
Mathematical models
Meteorology
Numerical prediction
Numerical weather forecasting
One dimensional models
Shallow water
Shallow water equations
Studies
Weather forecasting
Well posed problems
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The aim of this paper is to investigate the feasibility of well-posed lateral boundary conditions in a Fourier spectral semi-implicit semi-Lagrangian one-dimensional model. Two aspects are analyzed: (i) the complication of designing well-posed boundary conditions for a spectral semi-implicit scheme and (ii) the implications of such a lateral boundary treatment for the semi-Lagrangian trajectory computations at the lateral boundaries. Straightforwardly imposing boundary conditions in the gridpoint-explicit part of the semi-implicit time-marching scheme leads to numerical instabilities for time steps that are relevant in today's numerical weather prediction applications. It is shown that an iterative scheme is capable of curing these instabilities. This new iterative boundary treatment has been tested in the framework of the one-dimensional shallow-water equations leading to a significant improvement in terms of stability. As far as the semi-Lagrangian part of the time scheme is concerned, the use of a trajectory truncation scheme has been found to be stable in experimental tests, even for large values of the advective Courant number. It is also demonstrated that a well-posed buffer zone can be successfully applied in this spectral context. A promising (but not easily implemented) alternative to these three above-referenced schemes has been tested and is also presented here. [PUBLICATION ABSTRACT]
ISSN:0027-0644
1520-0493
DOI:10.1175/2008MWR2539.1