Coupling the Hexagonal B1-grid and B2-grid to Avoid a Computational Mode Problem of the Hexagonal ZM-grid

抄録

A shallow water model is developed on the regular hexagonal mesh by combining the hexagonal B1-grid and B2-grid schemes. The new scheme called as the hexagonal synchronized B-grid (SB-grid) scheme in this work allows avoiding a computational mode problem of the ZM-grid scheme. It is known that the problem is caused by the mismatch of degrees of freedoms of the prognostic variables. The SB-grid uses the same variable arrangement as the ZM-grid, placing fluid depths and fluid velocities at the centers and corners of hexagonal cells, respectively, but the nonlinear terms of the momentum equation are discretized using wider spatial stencils than those of the ZM-grid. This change results in the inhibition of extra interactions in the velocity fields that enhances a computational mode in the ZM-grid. Geostrophic adjustment tests on a regular hexagonal mesh confirm that the SB-grid shallow water model behaves almost equivalently to the Z-grid model, and the computational mode problem is certainly settled down.