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A systematic method to enforce conservativity on semi‐Lagrangian schemes

Semi‐Lagrangian schemes have proven to be very efficient in modeling advection problems. However, most semi‐Lagrangian schemes are not conservative. Here, a systematic method is introduced in order to enforce the conservative property on a semi‐Lagrangian advection scheme. This method is shown to generate conservative schemes with the same linear stability range and the same order of accuracy as the initial advection scheme from which they are derived. We used a criterion based on the column‐balance property of the schemes to assess their conservativity property. We introduce an unsplit geometrical reconstruction that enforces conservativity. We show that this approach can be used with large Courant‐Friedrichs‐Lewy numbers and third‐order schemes. We give a physical application in the case of the Rayleigh‐Taylor instability.