大气对流的对称性保持JFNK方法的评价
Assessment of a symmetry preserving JFNK method for atmospheric convection
摘要：
基于线性解耦半隐式或全隐式技术的非静力大气流动的数值模拟，通常通过预条件Krylov方法来求解线性系统，而不保持对流算子的斜对称性。我们建议进行大气模拟，在这样一个全隐式的方式，差分算子既保持斜对称性和紧密的非线性耦合的微分算子。我们证明了一个保持守恒的无雅可比的Newton-Krylov~（JFNK）方法模拟了对流输运和湍流耗散之间的平衡。我们提出了一个小波方法作为一个有效的对称性保持离散化技术。本文用两个穿透对流的基准模拟检验了求解非静力大气流动方程的保精度JFNK方法：a）中性层结和稳定层结环境中的干热气流上升，（b）结果表明，涡动粘性系数模式能较好地模拟城市热岛环流对地面热通量$H_0$的影响，其影响范围为$25 \le H_0 \le 930$ Wm $^{-2}$的亚网格尺度模式的必要的耗散，而保密JFNK方法提供了一个令人满意的水平的质量和能量守恒。从实验室实验的热岛环流和现场测量的潜在温度的结果的比较也表明，目前的节能JFNK框架的建模精度。
英文摘要：
Numerical simulations of nonhydrostatic atmospheric flow, based on linearly decoupled semi-implicit or fully-implicit techniques, usually solve linear systems by a pre-conditioned Krylov method without preserving the skew-symmetry of convective operators. We propose to perform atmospheric simulations in such a fully-implicit manner that the difference operators preserve both the skew-symmetry and the tightly nonlinear coupling of the differential operators. We demonstrate that a symmetry-preserving Jacobian-free Newton-Krylov~(JFNK) method mimics a balance between convective transport and turbulence dissipation. We present a wavelet method as an effective symmetry preserving discretization technique. The symmetry-preserving JFNK method for solving equations of nonhydrostatic atmospheric flows has been examined using two benchmark simulations of penetrative convection -- a) dry thermals rising in a neutrally stratified and stably stratified environment, and b) urban heat island circulations for effects of the surface heat flux $H_0$ varying in the range of $25 \le H_0 \le 930$Wm$^{-2}$.The results show that an eddy viscosity model provides the necessary dissipation of the subgrid-scale modes, while the symmetry-preserving JFNK method provides the conservation of mass and energy at a satisfactory level. Comparisons of the results from a laboratory experiment of heat island circulation and a field measurement of potential temperature also suggest the modelling accuracy of the present symmetry-preserving JFNK framework.
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