Multidimensional method-of-lines transport for atmospheric flows over steep terrain using arbitrary meshes
Multidimensional method-of-lines transport for atmospheric flows over steep terrain using arbitrary meshes
复制标题
DOI：
10.1016/j.jcp.2017.04.061
复制
发表时间：
2017-02
期刊：
影响因子：
--
通讯作者：
James Shaw;H. Weller;J. Methven;T. Davies
中科院分区：
文献类型：
--
作者：
James Shaw;H. Weller;J. Methven;T. Davies
将地形包括在大气模式中会引起下边界附近的网格扭曲，这可能会降低精度，并对运输方案的稳定性构成挑战。多维传输格式避免了在扭曲的任意网格上分裂误差，而线方法格式由于在定点进行重建而具有较低的计算成本，本文提出了一种在任意网格上数值稳定的多维线方法有限体积传输格式“cucuicFit”。由冯·诺依曼稳定性分析得出的稳定性条件在模型初始化过程中被施加，以在网格的扭曲区域和陡峭的下边界附近获得稳定性并提高精度。重建计算只依赖于网格，每个时间阶段每个面只需要一个矢量乘法，而不考虑速度场。立方体拟合方案通过三个理想的数值测试进行评估。第一个是在严重扭曲的地形跟随网格上进行的标准水平传输测试的变体。第二个是新的测试用例，通过在地形跟随网格、切割单元网格和新的倾斜单元网格上在陡峭地形的下边界处传输示踪剂来评估地面附近的精度，这些网格不受与切割单元相关的严格时间步长限制。第三，标准测试使六角二十面体网格和立方体球面网格上的涡流中的示踪物变形。在所有测试中，cuiticFit是稳定的，并且在很大程度上对网格扭曲不敏感，并且cuiticFit的结果比使用多维线性迎风传输方案获得的结果更准确。无论网格是否扭曲，CucuicFit格式都是二阶收敛的。
Including terrain in atmospheric models gives rise to mesh distortions near the lower boundary that can degrade accuracy and challenge the stability of transport schemes. Multidimensional transport schemes avoid splitting errors on distorted, arbitrary meshes, and method-of-lines schemes have a low computational cost because they perform reconstructions at fixed points.This paper presents a multidimensional method-of-lines finite volume transport scheme, “cubicFit”, which is designed to be numerically stable on arbitrary meshes. Stability conditions derived from a von Neumann stability analysis are imposed during model initialisation to obtain stability and improve accuracy in distorted regions of the mesh, and near steeply-sloping lower boundaries. Reconstruction calculations depend upon the mesh only, needing just one vector multiply per face per time-stage irrespective of the velocity field.The cubicFit scheme is evaluated using three, idealised numerical tests. The first is a variant of a standard horizontal transport test on severely distorted terrain-following meshes. The second is a new test case that assesses accuracy near the ground by transporting a tracer at the lower boundary over steep terrain on terrain-following meshes, cut-cell meshes, and new, slanted-cell meshes that do not suffer from severe time-step constraints associated with cut cells. The third, standard test deforms a tracer in a vortical flow on hexagonal–icosahedral meshes and cubed-sphere meshes. In all tests, cubicFit is stable and largely insensitive to mesh distortions, and cubicFit results are more accurate than those obtained using a multidimensional linear upwind transport scheme. The cubicFit scheme is second-order convergent regardless of mesh distortions.