R. Mittal has developed during her Ph.D. at IIT Delhi and LMD a positive definite advection scheme on hexagonal-icosahedral grids (Mittal et al., 2007). It is a finite volume scheme where the hexagons are the control volumes. As in LMD-Z, monotonicity results from the use of slope limiters (Hourdin & Armengaud, 1999).

Test Case : Deformational Flow

Analytic solution

Numerical solution with 10242 cells