In many applications, uncertainty in problem data leads to the need for numerous computationally expensive simulations. This report addresses this challenge by developing a penalty-based ensemble algorithm. Building upon Jiang and Layton's work on ensemble algorithms that use a shared coefficient matrix, this report introduces the combination of penalty methods to enhance its capabilities. Penalty methods uncouple velocity and pressure by relaxing the incompressibility condition. Eliminating the pressure results in a system that requires less memory. The reduction in memory allows for larger ensemble sizes, which give more information about the flow and can be used to extend the predictability horizon.

翻译：在许多应用中，问题数据的不确定性导致需要进行大量计算成本高昂的模拟。本报告通过开发一种基于惩罚的系综算法来应对这一挑战。基于Jiang和Layton在利用共享系数矩阵的系综算法方面的工作，本报告引入了惩罚方法的组合以增强其能力。惩罚方法通过松弛不可压缩条件来解耦速度与压力。消除压力后得到的系统所需内存更少。内存的减少允许更大的系综规模，从而提供更多关于流动的信息，并可被用于延长可预测性时间范围。