A MASS-CONSERVING SEMI-LAGRANGIAN SCHEME FOR THE SHALLOW-WATER EQUATIONS

By generalizing the algorithm of Priestley for passively advected fiel ds, a mass-conserving scheme for the coupled shallow-water equations i s obtained. It is argued that the interpolation step of semi-Lagrangia n schemes is the principal reason for their lack of formal conservatio n. The corrections introduced by the proposed algorithm to achieve con servation appropriately reflect the localized nature of the interpolat ion errors that induce its violation.