能量守恒的自适应网格模式在南海月平均流计算中的应用

本文在正压原始方程的基础上发展了一套适用于自适应网格坐标的自适应网格模式。该模式保持了笛卡尔坐标系下原有的整体积分性质。由于自适应网格与计算区域边界相重合，因而该模式可用于具有复杂形状的区域边界的计算问题。本文将其用于南海月平均流的数值模拟，取得了良好的效果。     

自适应网格与均匀网格在数值模拟中的对比研究

采用自适应网格和均匀网格两种模式，对1996年8月3—4日发生在山西、河北、河南三省交界地区的暴雨个例进行模拟和对比研究。结果表明，自适应网格模式对所关心的天气系统及其降水的模拟精度高于均匀网格，特别是对降水、风场、急流、涡度场的模拟精度改善显著。这说明自适应网格模拟的中尺度系统特征更清晰。     

完全保持能量守恒的非常定自适应网络模式

本文基于自适应网络的原理，发展了一套网格随时间变的自适应网格模式。该模式保持着ＩＡＰ模式原有的整体积分性质，并具有在任何时刻可随意调整网格点的疏密程度及网格点与边界相重合的特点，可用于台风路径的数值预报等方面。     

自适应网格模式在暴雨数值模拟中的应用

基于变分原理，自适应网格技术能根据数值模式的特点，在模式解梯度大的地区自动加密网格，提高模式的分辨率。将其应用于MM4模式中，采用多重网格法以加速自适应网格的生成。对1996年8月4日至5日发生在华北的特大台风暴雨过程，用自适应网格模式和均匀网格模式进行了数值模拟和动力诊断分析，以研究自适应网格模式在天气预报和模拟应用中的特点。试验表明，采用自适应网格后计算稳定，对所关心的天气系统及其降水的模拟精度均高于均匀网格模式，对形势场、风场的模拟精度也有明显改善。     

自适应网格在大气海洋问题中的初步应用

自适应网格法是80年代兴起的通过求解椭圆型方程的边值问题来数值生成网格的一种新方法。它是在任意形状的区域上求偏微分方程的数值解的一种非常有效的工具。该方法抛弃了等距均匀的差分网格，代之以能够自动地适应所研究问题中解的特征的疏密程度不均的曲线网格。如在边界上计算网格与实际边界相重合，在区域内部可任意调节网格点的疏密程度等。本文扼要地介绍了自适应网格的原理及其构造方法。并将其应用于生成南海区域的计算网格以及数值预报台风路径的自适应网格。     

自适应网格技术在MM5中的应用研究

结合一次暴雨过程，将自适应网格技术应用于中尺度模式MM5中进行数值试验，同时对比自适应网格方案和固定网格方案的优劣，对模拟结果作了诊断分析。结果表明：对于此次降水过程，自适应网格模拟的效果取决于一些参数的选择。     

非常定自适应网格模式在台风路径数值预报中的应用

本文将作者在前文中介绍的非常定自适应网格模式用于台风路径的数值预报。由于自适应网格在台风中心附近安排了较密的网格，有效地提高了网格的分辨率，使得台风环流的结构在预报48小时以后仍能保持，其预报的路径与实况相比令人鼓舞。     

Gerris数值方案及其在海洋数值模拟中的应用

基于动态自适应网格的开源软件Gerris受到越来越多海洋和水文研究者的关注.概述了Gerris开发背景、研究现状和特点,详细阐述了Gerris数值方案,包括动态自适应网格、动态负载平衡技术原理、广义正交曲线坐标系、内嵌复杂固体边界和地形数据的处理方法,并探讨了Gerris在海洋数值模拟中的初步应用.结果表明,Gerris动态自适应网格在多尺度问题模拟中的优势独特,在海洋数值模拟应用中可通过自适应网格提高地理特征的精度,通过GTS(或KDT)格式的数据来处理地形和网格,达到同时兼顾精确性和易用性的目的,使得Gerris与其他海洋模式进行有机结合成为重要发展方向.     

多重网格法在MM5自适应模式中的应用

将多重网格法应用于MM5中来加速自适应网格的生成,并用这种方法来模拟2002年6月17-18日发生在江南和华南的暴雨过程。试验表明：在收敛精度要求高的情况下自适应模式模拟结果的精度高于均匀网格模式,且多重网格法有助于提高运算效率。     

河北省变网格数值预报系统设计和试验

设计了一种将原ＭＭ４模式的均匀网格变换成非均匀网格的方案,构造了一套适合河北省特点的变网格预报模式,同时建立了一套可投入业务使用的变网格数值预报系统,最后通过一次暴雨过程的模拟分析,证明变网格数值预报优于均匀网格数值预报     

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

An adaptive 2 D 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 pointwise 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, terrainfollowing 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 coarsefine 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.     

多重网格法在加速自适应网格生成中的应用

多重网格法是70年代以来发展起来的用于加速迭代收敛的一种行之有效的方法,它通过采用不同疏密的网格距来“消除”不同频率范围内的误差分量的办法,加速了迭代的收敛速度,具有收敛速度快, 收敛精度高以及节省CPU时间等特点。将其用于台风路径预报的自适应网格的生成,试验表明,多重网格法比单重网格可提高效率达20多倍。     

A Variable Mesh Spacing for Large-Eddy Simulation Models in the Convective Boundary Layer

A variable vertical mesh spacing for large-eddy simulation (LES) models in a convective boundary layer (CBL) is proposed. The argument is based on the fact that in the vertical direction the turbulence near the surface in a CBL is inhomogeneous and therefore the subfilter-scale effects depend on the relative location between the spectral peak of the vertical velocity and the filter cut-off wavelength. From the physical point of view, this lack of homogeneity makes the vertical mesh spacing the principal length scale and, as a consequence, the LES filter cut-off wavenumber is expressed in terms of this characteristic length scale. Assuming that the inertial subrange initial frequency is equal to the LES filter cut-off frequency and employing fitting expressions that describe the observed convective turbulent energy one-dimensional spectra, it is feasible to derive a relation to calculate the variable vertical mesh spacing. The incorporation of this variable vertical grid within a LES model shows that both the mean quantities (and their gradients) and the turbulent statistics quantities are well described near to the ground level, where the LES predictions are known to be a challenging task.     

Towards Adaptive Grids for Atmospheric Boundary-Layer Simulations

We present a proof-of-concept for the adaptive mesh refinement method applied to atmospheric boundary-layer simulations. Such a method may form an attractive alternative to static grids for studies on atmospheric flows that have a high degree of scale separation in space and/or time. Examples include the diurnal cycle and a convective boundary layer capped by a strong inversion. For such cases, large-eddy simulations using regular grids often have to rely on a subgrid-scale closure for the most challenging regions in the spatial and/or temporal domain. Here we analyze a flow configuration that describes the growth and subsequent decay of a convective boundary layer using direct numerical simulation (DNS). We validate the obtained results and benchmark the performance of the adaptive solver against two runs using fixed regular grids. It appears that the adaptive-mesh algorithm is able to coarsen and refine the grid dynamically whilst maintaining an accurate solution. In particular, during the initial growth of the convective boundary layer a high resolution is required compared to the subsequent stage of decaying turbulence. More specifically, the number of grid cells varies by two orders of magnitude over the course of the simulation. For this specific DNS case, the adaptive solver was not yet more efficient than the more traditional solver that is dedicated to these types of flows. However, the overall analysis shows that the method has a clear potential for numerical investigations of the most challenging atmospheric cases.