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On numerical solution of the shallow water equations with chemical reactions on icosahedral geodesic grid

机译：二十面体测地线上具有化学反应的浅水方程的数值解

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摘要

The shallow water equations coupled to the set of reaction-advection-diffusion equations are discretized on a geodesic icosahedral mesh using the finite volume technique. The method of solution of this coupled system is based on the principle of semi-discretization. The algorithm is mass conserving and stable for advection with the Courant numbers up to 2.7. The important part of the methodology is the optimization of the node positions in the icosahedral grid. It is shown that a slight adjustment of the mesh is instrumental in improving the accuracy of the numerical approximation. The convergence of the approximation of the differential operators is evaluated and compared to the data published in the literature. Numerical tests performed with the shallow water solver include two advection experiments, steady and unsteady zonal balanced flow, mountain flow, and the Rossby wave. The mountain flow and the Rossby wave cases are used to test the transport properties of the method in the case of both passive and reactive scalar fields. The investigation of essential numerical characteristics of the method is concluded by the simulation of an unstable zonal jet. The numerical simulation is performed using the set of shallow water equations without dissipation as well as with the viscosity term added to the momentum equation. Results show that the behavior of the model is consistent with both the literature published on the subject and the general empirical evidence.
机译：使用有限体积技术，在测地二十面体网格上离散化了与反应-对流-扩散方程组耦合的浅水方程。该耦合系统的求解方法基于半离散化原理。该算法是质量守恒的，对流稳定，Courant数高达2.7。该方法的重要部分是优化二十面体网格中的节点位置。结果表明，对网格的轻微调整有助于提高数值逼近的准确性。评估了微分算子逼近的收敛性，并将其与文献中公布的数据进行了比较。用浅水求解器进行的数值试验包括两个对流实验，分别为稳定和非稳定的纬向平衡流，山区流和Rossby波。在无源标量场和无功标量场的情况下，均采用山流和Rossby波情况来测试该方法的传输特性。该方法的基本数值特性的研究是通过对不稳定的纬向射流的模拟得出的结论。使用没有耗散的浅水方程组以及将粘度项添加到动量方程组中进行了数值模拟。结果表明，该模型的行为与有关该主题的文献和一般经验证据均一致。

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