An Alternative Leapfrog Scheme for Surface Gravity Wave Equations

Abstract

An alternative leapfrog scheme using a staggered time grid system is proposed to solve surface gravity wave equations. In addition to the nondissipative second-order accuracy scheme that is inherent in the standard leapfrog scheme, the alternative leapfrog scheme has the advantages that 1) no separation of the solution occurs at the even and odd time levels, 2) it is twice as efficient as the standard leapfrog scheme, and 3) it requires only the one time level storage. Numerical experiments show its numerical properties and computational efficiency. The wave amplitude is not damped and the total energy is conserved. The alternative leapfrog scheme is one of the most efficient schemes. It is applied to the surface gravity wave terms in ocean circulation models, and its usefulness is shown.