CERFACS CERFACS Scientific Activity Report Jan. 2010 – Dec. 2011

LARGE SCALE ATMOSPHERIC COMPOSITION
FIG. 3.1: Distribution of the concentration of HOCl computed by the reduced model
3.2 A finite volume model for the advection of tracers on a sphere (D.
Cariolle, A. Praga, L. Giraud).
In the context of three-dimensionnal tracer advection on the sphere, as discussed in the previous section, we
are studying finite-volume schemes on an area-preserving grid. The objective is to develop an efficient mass
conservative scheme with a good scalability on HPC that will be coupled to the chemical solver described
in section 3.1. In order to avoid the problem of convergence of the longitudes at the poles, the adopted grid
conserves an equally spacing of the latitudes but, from equator to pole, reduces progressively the number
of points on each latitudinal circle. The number of point on each latitude is chosen to obtain model cells
that have approximatively the same surface, so that for a given velocity vector the maximum possible time
step is uniform all over the globe. Grid properties are set by specifying a reference cell at the equator. In
our preliminary tests , a cell of 1 ◦ by 1 ◦ was used.
On that grid the bidimensionnal advection is done by successive transports in each direction. For each onedimensionnal
case, we use a finite volume scheme, a standard scheme in the climate modelling community.
We chose a Van Leer’s second-order scheme, which is accurate and conservative by construction.
Comparison with others schemes such as Prather’s or Godunov’s makes it interesting in terms of the
accuracy/storage ratio. With slope limitations, we also ensure positivity of the solution, a property that
is required for subsequent coupling with the chemical solver.
A first implementation was done as a sequential version in Matlab. The scheme was integrated on a standard
test suite where winds and concentrations have analytical solutions. This allows us to check the performance
188 Jan. 2010 – Dec. 2011