Penalty Ensembles for Navier-Stokes with Random Initial Conditions and Forcing

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.