Abstract

This study presents the development of an unstructured adaptive finite-element model (Fluidity-Atmosphere) for atmospheric research. Fluidity is a computational fluid-dynamics open source model capable of numerically solving the 3D compressible Navier-Stokes equation using a dynamically adaptive mesh. To evaluate the performance of adaptive meshes and cloud microphysics parameterisation in Fluidity-Atmosphere, the convection test case has been setup and the unstructured tetrahedral meshes are adapted automatically with the solutions of velocity and potential temperature in time and space. To couple the physical parameterisations with the 3D anisotropic unstructured mesh in Fluidity-Atmosphere, a mesh-redistribution scheme has been designed. The simulation provides the structures of the disturbance similar to the real convections; realistic horizontal velocity fields having inflow concentrated near the surface and outflow in the upper domain. To improve the computational efficiency, an “onom” Local-Galerkin method is designed which is a family of the variants of spectral element method, employing nth-degree piecewise polynomials for the field representation while mth-degree polynomials for the flux representation. We will introduce five onom schemes and analyze the dispersion relations and the accuracy by homogeneous advection tests. The results have shown that the dispersion errors are smaller than the classical fourth-order finite difference schemes and the uniform nth-order accuracy is kept by onon scheme.