Linear advection modelling: the issue of divergent flows

Schemes for linear advection modelling in multiple dimensions on structured grids use either time-splitting or an unsplit approach for flux computation. In the case of strongly divergent flows, time-splitting introduces anisotropy in the solution whereas, with the unsplit approach, more mass than actually available may be abstracted from the computational cells, leading for instance to oscillations and sometimes instability. A simple correction for the flux, taking into account the divergence of the flow, is proposed to eliminate the problem for the unsplit approach. This correction introduces a limitation on the computational time step. An experiment carried out using a market-available software package shows that the problem above is of practical interest, and that verification procedures of modelling software should take into account simulations under non-uniform flows.