An Accurate Semi-Lagrangian Scheme with a Unified Interpolation Function Constructed from Vorticity and Velocity Components

抄録

For atmospheric and oceanic modeling, the equations of motion are numerically solved in either momentum form or vorticity form. Since vorticity is a conservative quantity in the Lagrangian sense, it has been considered that the vorticity form discretization scheme is more appropriate for the simulation of atmospheric and oceanic flows. However, it requires a Poisson solver to obtain the streamfunction from the vorticity: the use of a Poisson solver is thought to be a drawback for high-resolution atmospheric and oceanic modeling. In contrast, a Poisson solver is not required if the momentum form discretization scheme is applied to compressible flows. In this study, we propose a new advection scheme which possesses the advantages of both schemes: conservation of vorticity and no need for a Poisson solver. Both velocity components and vorticity are temporally integrated using the semi-Lagrangian method by constructing a unified interpolation function for velocity components and vorticity. We apply this scheme to a two-dimensional shear instability problem, and have found that this scheme gives a result competitive with the vorticity form scheme and is more accurate than the momentum form scheme.