论文标题
在周期性域上的表面Quasi地球地面流动的数值模拟
Numerical Simulations of Surface-Quasi Geostrophic Flows on Periodic Domains
论文作者
论文摘要
我们提出了一种新型算法，用于通过非线性偏微分方程偶联转运和分数扩散现象建模的表面Quasi Geostrophic（SQG）流。时间离散化包括一个明确的强稳定性保护三阶段runge-kutta方法，而磁通校正的转机（FCT）方法以及分数运算符的Dunford-Taylor表示，用于空间离散化。使用标准连续的分段线性有限元素，并且该算法对网格结构或计算域没有限制。在Inviscid情况下，我们表明所得方案在标准CFL条件下满足离散的最大原理属性，并在实践中观察其在太空中的二阶精度。该算法成功地近似几个基准，具有尖锐的过渡和典型的SQG流量的精细结构。另外，在自由腐烂的大气湍流模拟中观察到理论上的kolmogorov能量衰减速率。
We propose a novel algorithm for the approximation of surface-quasi geostrophic (SQG) flows modeled by a nonlinear partial differential equation coupling transport and fractional diffusion phenomena. The time discretization consists of an explicit strong-stability-preserving three-stage Runge-Kutta method while a flux-corrected-transport (FCT) method coupled with Dunford-Taylor representations of fractional operators is advocated for the space discretization. Standard continuous piecewise linear finite elements are employed and the algorithm does not have restrictions on the mesh structure nor on the computational domain. In the inviscid case, we show that the resulting scheme satisfies a discrete maximum principle property under a standard CFL condition and observe, in practice, its second-order accuracy in space. The algorithm successfully approximates several benchmarks with sharp transitions and fine structures typical of SQG flows. In addition, theoretical Kolmogorov energy decay rates are observed on a freely decaying atmospheric turbulence simulation.
