数值天气预报中相容有限元格式的能量守恒SUPG方法
Energy conserving SUPG methods for compatible finite element schemes in numerical weather prediction
摘要：
我们提出了一个能量守恒的空间离散的基础上的泊松括号，可用于推导干燥的可压缩欧拉方程以及热浅水方程。它是使用兼容的有限元法制定的，并扩展了Wimmer，Cotter和Bauer（2019）中描述的浅水方程的迎风合并。而前者是限制DG迎风，能量守恒SUPG计划（部分）连续的Galerkin热场空间是新引进的。通过将基于泊松括号的空间离散化耦合到能量守恒的时间离散化，验证了能量守恒的性质。此外，离散化被证明是导致一个改进的温度场发展的稳定性时，包括上绕。还提出了一种近似节能的全离散化，具有较小的计算成本。
英文摘要：
We present an energy conserving space discretisation based on a Poisson bracket that can be used to derive the dry compressible Euler as well as thermal shallow water equations. It is formulated using the compatible finite element method, and extends the incorporation of upwinding for the shallow water equations as described in Wimmer, Cotter, and Bauer (2019). While the former is restricted to DG upwinding, an energy conserving SUPG scheme for the (partially) continuous Galerkin thermal field space is newly introduced here. The energy conserving property is validated by coupling the Poisson bracket based spatial discretisation to an energy conserving time discretisation. Further, the discretisation is demonstrated to lead to an improved temperature field development with respect to stability when upwinding is included. An approximately energy conserving full discretisation with a smaller computational cost is also presented.
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