LINEAR AND NONLINEAR SPLITTING SCHEMES CONSERVING TOTAL ENERGY AND MASS IN THE SHALLOW WATER MODEL
Three implicit and unconditionally stable difference schemes of the second order of approximation in all variables are presented for a shallow water model that takes into account the rotation and topography of the Earth. Two schemes are linear and one is nonlinear. The schemes are based on splitting the model equations into two one-dimensional subsystems. Each of the subsystems saves the mass and total energy both in differential and difference (in time and space) form. One of the linear schemes contains a smoothing procedure that does not violate the conservation laws and suppresses false oscillations caused by the use of central-difference approximations for spatial derivatives. The unique solvability of linear schemes and the convergence of iterations used to find their solutions are proved.