It is well documented that the direct solution of the primitive equation form (PE) of the shallow-water equations by conventional Galerkin finite elements fails to control numerical noise. While some alternative numerical techniques applied directly to the primitive equations have been successfully developed, a reformulation of the fundamental equations into the generalized wave continuity equation form (GWCE) provides an alternative noise-free procedure that has been used in numerous field applications. The selection of penalty parameter, ‘G’ for GWCE must, however, be carefully adjusted to achieve both mass balance and noise control. In this paper, a numerical method for solving the primitive equation with a filter is presented. It is shown that a filtered primitive equation method (FPE) controls numerical noise and is mass conservative. Since the FPE method derives its basis from observations about the behavior of GWCE, we present comparisons of the solution of the primitive equations via FPE with the solution of the wave equation via the GWCE form.
A filtered solution of the primitive shallow-water equations
Laible, J., & Lillys, T. P. (1997). A filtered solution of the primitive shallow-water equations. Advances in Water Resources, 23-35. https://doi.org/10.1016/S0309-1708(96)00013-9