ON A STUDY OF STAGGERED LEAPFROG SCHEME FOR LINEAR SHALLOW WATER EQUATIONS

L. Krismiyati Budiasih, L. Hari Wiryanto

  DOI:  https://doi.org/10.37418/amsj.9.11.88

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In this paper, we present an analytical and numerical study of staggered leapfrog scheme for linear shallow water equation. It is shown that the scheme is stable when Courant number < 1, has second order accurate in both time and space, and there is no damping error in this scheme. We implement the scheme to simulate standing wave in a closed basin to show that the surface motions stay zero in a node and have constant amplitude at the antinode. For an external force given into the basin, it will induce a resonance, which cause the wave amplitude is getting bigger at the position of antinode. Moreover, we simulate a wave in a tidal basin, and show that the model has infinite spin up time. For a linear shallow water equation with linear friction, it is shown that the model has finite spin up time.

Keywords: leapfrog method, shallow water equations, tidal basin.