Second order accuracy of two-time level semi-Lagrangian schemes
Gospodinov, I.-G. ; Spiridonov, V.-G. ; J.F. Geleyn, J.-F.
Année de publication
2001
The accuracy of the two-time-level semi-Lagrangian semi-implicit time
integration scheme is analysed. Two relatively independent problems are
identifiedthe discretization of the implicit trajectory equation and
the treatment of the nonlinear residual. Two theorems giving conditions
for second-order accuracy of the two-time-level semi-Lagrangian
semi-implicit scheme are stated. As a result, a new scheme for the
trajectory equation is proposed and a class of schemes for the nonlinear
residual, which are second-order accurate in time, are introduced. A
simplified one-dimensional shallow water' model is developed in order
to test the proposed scheme in comparison with other, previously known,
ones. Some experiments proving stability, accuracy and conservation
ability are presented.</div>
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