Modellierung und Approximation feuchter atmosphärischer Strömungen unter Berücksichtigung topographischer Effekte

在流体动力学中，守恒性质吸引了大量的注意力。在潮湿过程的存在下，相边界可以用不连续面来模拟。因此，一个数学上合适的公式是弱形式的质量、动量和能量守恒定律。在气象建模中，存在许多替代公式，这些公式允许以某种方式处理不连续性的简单离散化。在这个项目中，我们比较质量和动量守恒的方法，不同的热力学过程的描述。我们考虑和比较两个不同类别的有限体积法：波传播方法（其中的数值通量是基于当地黎曼问题的解决方案）和传统上用于数值天气预报（NWP）的方法（其中在每个组件中的通量是通过插值获得）。为了解决气象问题的一些成功的前景数值方法应该能够科普地形，小马赫数和弗劳德数，以及与刚性相变过程。我们使用笛卡尔网格离散化，包括嵌入边界处的切割单元。

In fluid dynamics conservation properties attract a great deal of attention. In the presence of moist processes phase boundaries can be modelled by discontinuities. Therefore a mathematically appropriate formulation are the conservation laws for mass, momentum and energy in weak form. In meteorological modelling there exist numerous alternative formulations which allow for simple discretisations taking care of discontinuities in one way or another. In this project we compare mass- and momentum conserving methods which differ in their description of thermodynamic processes. We consider and compare two different classes of finite volume methods: wave-propagation methods (where the numerical flux is based on the solution of local Riemann problems) and methods which are traditionally used in numerical weather prediction (NWP) (where in each component the flux is obtained by interpolation). To address meteorological problems with some prospect of success numerical methods should be able to cope with orography, small Mach- and Froude numbers, as well as with stiff phase transition processes. We use discretisations on Cartesian grids including cut cells at embedded boundaries.