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Conservative semi-Lagrangian transport schemes

An illustration of the geometric construction of SLICE (Semi-Lagrangian Inherently Conserving and Efficient).

SLICE (Semi-Lagrangian Inherently Conserving and Efficient) is a semi-Lagrangian transport scheme that inherently conserves mass.

SL transport schemes are known to be highly efficient as they provide the possibility of using large time steps without any stability constraints. Traditionally SL schemes have been based on interpolation, to compute fields of an irregular (Lagrangian) grid from those given on an underlying regular (Eulerian) grid. However, the interpolation operation does not conserve properties of the field, in particular mass. Therefore, an SL based transport scheme does not generally conserve mass of the transported species.

Some applications do not need exact mass conservation, e.g. NWP for which the integration period is relatively short. Others, such as climate and chemistry applications, require exact mass conservation, otherwise considerable errors can accumulate during relatively long simulations - leading to unphysical behaviours.

SLICE keeps the advantage of the unconditional stability of an SL scheme while removing its drawback of lack of mass conservation. Instead of using a non-conservative interpolator to transfer information from the Eulerian grid to the Lagrangian one, SLICE uses a conservative remapping.

In general, conservative remappings are based on finite/control volume approaches rather than grid points. They remap (integrate) fields from regular, underlying Eulerian cells to irregular Lagrangian cells. This requires computation of all the geometric details of intersections between the Lagrangian and Eulerian grids. This computational overhead has been a major obstacle to applying conservative remappings, especially in higher dimensions.

An important feature of SLICE is that it avoids this prohibitive geometric overhead by using a flow-dependent splitting strategy. For instance, it reduces a full three-dimensional remapping into three simple one-dimensional remappings. This splitting also contributes to the flexibility of SLICE to use high-order schemes without prohibitive computational overheads.

Key aims

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