基于特征正交分解与离散经验插值的浅水波模式降阶解法

利用特征正交分解方法(proper orthogonal decomposition method,POD)与离散经验插值方法(discrete empirical interpolation method,DEIM)对旋转大气中有限区域浅水波模式进行降阶处理,获得浅水波模式的POD/DEIM降阶模型(ROM)及其数值解,评估降阶模型刻画大尺度大气系统的能力和效率。研究结果表明:POD/DEIM降阶模型从根本上实现了浅水波模式降阶,提高了计算效率,降低了计算代价。POD/DEIM降阶模型的计算效率明显高于POD降阶模型和全阶模型,并且可以捕获全阶模型超过99. 8%的能量。特别当空间格点数量明显增加时,POD/DEIM降阶模型CPU耗时很少。但POD/DEIM降阶模型模拟质量依赖于瞬像维数和DEIM插值点维数两个可变参数,并且DEIM插值点数量减少会明显缩短POD/DEIM降阶模型的CPU耗时。

Reduced-order Modelling for Shallow-water Equations Model via Proper Orthogonal Decomposition and Discrete Empirical Interpolation

The reduced-order modelling problem was addressed by considering a nonlinear shallow-water equations model with limited-area region in rotating atmosphere. The proper orthogonal decomposition method (POD) and the discrete empirical interpolation method (DEIM) were used to establish the reduced-order model (ROM), and then to obtain the numerical solutions, to evaluate the capability and efficiency of simulating large-scale atmospheric motion. The study shows that the ROM fundamentally improves the computational efficiency and reduces the computation cost. The computational efficiency of the ROM based on POD/DEIM is significantly higher than that based on POD and the full-order model. The ROM based on POD/DEIM can capture more than 99.8% energy of the full-order model. It consumes very little CPU time, especially when the quantity of spatial grids obviously increases. However, the simulation quality of the ROM based on POD/DEIM relies on the choices of the dimension of snapshots and DEIM interpolation points. As the dimension of the DEIM interpolation points is decreased, the CPU time cost of the reduced-order model based on POD/DEIM will be reduced obviously.