An Adaptive Nonhydrostatic Atmospheric Dynamical Core Using a Multi-Moment Constrained Finite Volume Method

Abstract

An adaptive 2D nonhydrostatic dynamical core is proposed by using the multi-moment constrained finite-volume (MCV) scheme and the Berger-Oliger adaptive mesh refinement (AMR) algorithm. The MCV scheme takes several point-wise values within each computational cell as the predicted variables to build high-order schemes based on single-cell reconstruction. Two types of moments, such as the volume-integrated average (VIA) and point value (PV), are defined as constraint conditions to derive the updating formulations of the unknowns, and the constraint condition on VIA guarantees the rigorous conservation of the proposed model. In this study, the MCV scheme is implemented on a height-based, terrain-following grid with variable resolution to solve the nonhydrostatic governing equations of atmospheric dynamics. The AMR grid of Berger-Oliger consists of several groups of blocks with different resolutions, where the MCV model developed on a fixed structured mesh can be used directly. Numerical formulations are designed to implement the coarse-fine interpolation and the flux correction for properly exchanging the solution information among different blocks. Widely used benchmark tests are carried out to evaluate the proposed model. The numerical experiments on uniform and AMR grids indicate that the adaptive model has promising potential for improving computational efficiency without losing accuracy.

摘要

本文提出了一种基于多矩限制有限体积法和Berger-Oliger自适应加密网格的二维非静力大气动力框架。多矩限制有限体积法算法在每个计算单元内选择多个点值作为预报量,利用独立单元上的局地高阶重构构造高精度的数值格式。多矩限制有限体积法算法定义了两种类型的矩,即积分平均值矩和点值矩,它们作为限制条件约束预报量的更新,其中对积分平均值矩的限制条件保证了数值格式的严格守恒性。本文在基于高度和地形跟踪的变分辨率网格上采用多矩限制有限体积法算法求解非静力大气运动方程,其中所使用的Berger-Oliger自适应加密网格是由几组具有不同分辨率的均匀网格块构成的,在固定的结构网格上发展的多矩限制有限体积法算法可以直接在这些网格块上使用。我们还设计了粗细网格插值和通量修正的数值方法,使不同层网格块之间的信息得以双向交换。一些广泛使用的标准数值算例被用于检验本文所提出的模式,数值实验的结果表明,在保证数值精度的前提下,自适应模式对于提升计算效率具有可观的前景。