Mesh-free semi-Lagrangian methods for transport on a sphere using radial basis functions
Mesh-free semi-Lagrangian methods for transport on a sphere using radial basis functions
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DOI：
10.1016/j.jcp.2018.04.007
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发表时间：
2018-08-01
影响因子：
4.1
通讯作者：
Wright, Grady B.
中科院分区：
文献类型：
--
作者：
Shankar, Varun;Wright, Grady B.
本文提出了三种基于径向基函数（RBF）插值的半拉格朗日方法，用于球上输运的数值模拟。这些方法是无网格的，完全在笛卡尔坐标系中制定，从而避免了球体上人工边界处的任何不规则节点聚类，并自然绕过了与基于表面的坐标系相关的任何明显的人工奇点。对于在给定速度场中涉及示踪剂输运的问题，半拉格朗日框架允许这些新方法在时间积分期间避免使用任何稳定化项（如高粘度），从而减少了必须调整的参数的数量。这三种新的方法是基于插值使用1）全局RBF，2）局部RBF支架，和3）RBF划分的单位。对于后两种方法，我们发现，它是至关重要的，包括一些低次球谐插值。标准的测试用例组成的固体旋转和变形流的方法进行比较和对比，在其精度，效率，守恒特性，和耗散/分散误差。对于全局径向基函数，光谱空间收敛观察准均匀节点上的光滑解，而高阶精度观察局部径向基函数模板和分区的统一方法。(C)2018爱思唯尔公司All rights reserved.
We present three new semi-Lagrangian methods based on radial basis function (RBF) interpolation for numerically simulating transport on a sphere. The methods are mesh-free and are formulated entirely in Cartesian coordinates, thus avoiding any irregular clustering of nodes at artificial boundaries on the sphere and naturally bypassing any apparent artificial singularities associated with surface-based coordinate systems. For problems involving tracer transport in a given velocity field, the semi-Lagrangian framework allows these new methods to avoid the use of any stabilization terms (such as hyperviscosity) during timeintegration, thus reducing the number of parameters that have to be tuned. The three new methods are based on interpolation using 1) global RBFs, 2) local RBF stencils, and 3) RBF partition of unity. For the latter two of these methods, we find that it is crucial to include some low degree spherical harmonics in the interpolants. Standard test cases consisting of solid body rotation and deformational flow are used to compare and contrast the methods in terms of their accuracy, efficiency, conservation properties, and dissipation/dispersion errors. For global RBFs, spectral spatial convergence is observed for smooth solutions on quasi-uniform nodes, while high-order accuracy is observed for the local RBF stencil and partition of unity approaches. (C) 2018 Elsevier Inc. All rights reserved.