论文标题
在数值天气预测中兼容有限元方案的能源保护SUPG方法
Energy conserving SUPG methods for compatible finite element schemes in numerical weather prediction
论文作者
论文摘要
我们提出了基于泊松支架的节能空间离散化的，该托架可以用于推导干燥的可压缩欧拉和热浅水方程。它是使用兼容有限元法制定的，并扩展了Wimmer，Cotter和Bauer（2019）中所述的浅水方程的向上的融合。虽然前者仅限于DG上风，但此处新介绍了（部分）连续的Galerkin热场空间（部分）连续的Galerkin热场空间的SUPG方案。通过将基于泊松支架的空间离散化与能源保存时间离散化的耦合来验证能源保护财产。此外，当包括向上方向时，离散化被证明会导致稳定性的改善。还提出了近似能源保存全面离散化的计算成本。
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.
