Analysis of Apparent Topography Scheme for the Linear Wave Equation with Coriolis Force

Analysis of modified Godunov type schemes for the two-dimensional linear wave equation with Coriolis source term on cartesian meshes

“…In the present work we investigate the preservation of the geostrophic equilibrium in the context of the two-dimensional wave equation with Coriolis force (2), that is the linearised version of the shallow water equations. It generalises a study initiated in [3,4] in the one dimensional context. In Section 2 we recall the main characteristics of the wave equation with Coriolis force.…”

“…As for the velocity equations, either we keep the classical diffusion to obtain the Apparent Topography-Classical scheme (AT-C) or we delete diffusion terms which leads to the Apparent Topography-Low Froude scheme (AT-LF). In 1D, they are shown to be both stable and accurate [4]. ii.…”

“…The Apparent Topography scheme was introduced in [7], see also [8], to deal with the geostrophic equilibrium in the 1D nonlinear shallow water system. This strategy was proven to be stable in [4] for the 1D linear wave equation. Here we extend the procedure to the 2D linear wave equation.…”

“…with no Coriolis source term) is accurate for low M . It is no more the case when the Coriolis force is involved, see [3,4]. Indeed, in that case the diffusion on the pressure equation is shown to be responsible for the inaccuracy.…”