Solution of linearized rotating shallow water equations by compact schemes with different grid-staggering strategies

High accuracy solution of bi-directional wave propagation in continuum mechanics

“…In Table 1, Lele (2) refers to the discretisation scheme used in [15] to obtain the second derivative directly. The superscript (2) in the table refers to second derivative expressions.…”

“…A fundamental example is the wave propagation equation in acoustics [2] given by the generic equation…”

“…Note that η is the displacement in the z-direction of the fluid surface above the mean or undisturbed height, H . Popular methods of solving shallow water equation available in published literature include, but are not limited to [7][8][9]1] and the references contained therein. In [1] and references contained therein, the linearised rotational shallow water equation (LRSWE) has been solved by compact schemes in different grids given in [9] by solving these three equations.…”

“…Popular methods of solving shallow water equation available in published literature include, but are not limited to [7][8][9]1] and the references contained therein. In [1] and references contained therein, the linearised rotational shallow water equation (LRSWE) has been solved by compact schemes in different grids given in [9] by solving these three equations. A specially designed staggered compact scheme was found to be the best among all the schemes studied in this reference with the help of four-stage fourth order Runge-Kutta (RK4) method; two time-level forward-backward (FB) [10] and four time-level generalised FB temporal integration schemes [11,12].…”

“…As BDWE represents non-dissipative, non-dispersive dynamics, we also consider the canonical problem of linearised rotating shallow water equation (LRSWE) in a new formulation involving second order derivative in time, which represents dispersive waves along with a stationary mode. The computations of LRSWE with RK4 and RKN methods for temporal discretisation and Lele's compact schemes for spatial discretisation are compared with computations performed with RK4 method for time discretisation and staggered compact scheme (SCS) for spatial discretisation by treating it as a set of three equations as reported in Rajpoot et al (2012) [1].…”