A modified hybrid finite‐element method for a semi‐implicit mass‐based non‐hydrostatic kernel

Abstract

AbstractA hybrid finite‐element vertical discretization method for a semi‐implicit mass‐based non‐hydrostatic kernel is a feasible high‐order discretization approach which combines the advantages of both finite‐differential and finite‐element methods. In this article, we put forward a modified version of the existing hybrid finite‐element method to reduce computation load and improve precision. A key feature of our modified method is the presence, in the enlarging step, of new levels which are not equally spaced, but rather based on Gaussian quadrature. A higher‐order accuracy may be thus achieved with less enlarged levels by virtue of the properties of Gaussian quadrature. The modified method is also designed to fulfil the constraints required by the dynamic kernel, which themselves are crucial to ensure stability. A set of 2D and 3D test cases are conducted so as to confirm the accuracy and the stability of the new method.