V. Casulli et E. Cattani, STABILITY, ACCURACY AND EFFICIENCY OF A SEMIIMPLICIT METHOD FOR 3-DIMENSIONAL SHALLOW-WATER FLOW, Computers & mathematics with applications, 27(4), 1994, pp. 99-112
The stability analysis, the accuracy and the efficiency of a semi-impl
icit finite difference scheme for the numerical solution of a three-di
mensional shallow water model are presented and discussed. The governi
ng equations are the three-dimensional Reynolds equations in which pre
ssure is assumed to be hydrostatic. The pressure gradient in the momen
tum equations and the velocities in the vertically integrated continui
ty equation are discretized with the theta-method, with theta being an
implicitness parameter. It is shown that the method is stable for 1/2
less than or equal to theta less than or equal to 1, unstable for the
ta < 1/2 and highest accuracy and efficiency is achieved when theta =
1/2 The resulting algorithm is mass conservative and naturally allows
for the simulation of flooding and drying of tidal flats.