Mass correction applied to semi-Lagrangian advection scheme

A simple mass correction is proposed for the semi-Lagrangian scheme using forward trajectories. The procedure includes (a) constructing the Lagrangian network induced by the motion of the fluid from the Eulerian network and finding the intersections of the networks by a general interpolation from the irregularly distributed Lagrangian grid to the regularly distributed Eulerian grid, (b) applying the spatial filter to remove the unwanted short waves and the values beyond the constraints, and finally (c) introducing a polynomial or sine function as the correction function that conserves mass while inducing the least modification to the results obtained from (a) and (b). Numerical simulations of pure advection, rotation, and idealized cyclogenesis show that the mass correction function does not degrade the accuracy of the results.