论文标题
用于非静态垂直大气动力学的精力平衡的准牛顿整合器
An energetically balanced, quasi-Newton integrator for non-hydrostatic vertical atmospheric dynamics
论文作者
论文摘要
提出了一个在球体上的非静态垂直大气动力学的能量平衡，隐式积分器。通过保留可压缩欧拉方程的非典型的哈密顿公式的偏斜对称性，集成剂可以使垂直大气运动的空间和时间之间的能量交换的确切平衡。积分器的性能通过降低内部线性系统维度的预处理策略加速。在这里，我们通过重复的Schur补体分解和仔细选择耦合项的速度将四个组件速度，密度，密度加权的电势温度和Exner压力系统降低到单一方程中，并仔细选择耦合项。正如当前所述，集成器基于水平垂直空间分裂，该空间分裂不允许底部地形。该集成剂已验证用于斜压不稳定性的标准测试用例和球体上的非静态重力波和高分辨率平面几何形状中的升高气泡，并在所有这些方案中显示出强大的收敛性。
An energetically balanced, implicit integrator for non-hydrostatic vertical atmospheric dynamics on the sphere is presented. The integrator allows for the exact balance of energy exchanges in space and time for vertical atmospheric motions by preserving the skew-symmetry of the non-canonical Hamiltonian formulation of the compressible Euler equations. The performance of the integrator is accelerated by a preconditioning strategy that reduces the dimensionality of the inner linear system. Here we reduce the four component velocity, density, density weighted potential temperature and Exner pressure system into a single equation for the density weighted potential temperature via repeated Schur complement decomposition and the careful selection of coupling terms. As currently formulated, the integrator is based on a horizontal-vertical spatial splitting that does not permit bottom topography. The integrator is validated for standard test cases for baroclinic instability and a non-hydrostatic gravity wave on the sphere and a rising bubble in a high-resolution planar geometry, and shows robust convergence across all of these regimes.
